Laxmi

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Determiners

Observe the nouns in the following sentences and words before them.

• An apple is a healthy fruit.
• Two cats have drunk a bowl of milk,
• My father has many cars.

Determiners are the words that introduce a noun and provide some information about it (but do not describe it). .
Determiners are followed by a noun.

• The ball
• Five cats
• His son
• Some students

Types of Determiners

• The quantifiers all, any, enough, less, a lot of, more, most, no, none of, some etc., are used with both countable and uncountable nouns.
• The quantifiers both, each, either, fewer, neither etc., are used only with countable nouns.

ARTICLES

Articles are bifurcated into
(i) Definite Article (the) and
(ii) indefinite articles (a, an).

(i) DEFINITE ARTICLE : When to use “THE”

❖ General Rules
Use the to refer to something which has already been mentioned.

Examples :
On Monday, an unarmed man stole 10,000 from the bank. The thief hasn’t been caught yet.
I was walking past Benny’s Bakery when I decided to go into the bakery to get some bread.

Use the when you assume there is just one of something in that place, even if it has not been mentioned before.

Examples :
We went on a walk in the forest yesterday.
Where is the bathroom?
Turn left and go to number 45. Our house is near the restaurant.
My father enjoyed the book you gave him.

(ii) INDEFINITE ARTICLES : When to use “a” and “an”.

In English, the two indefinite articles are a and an.
Like other articles, indefinite articles are invariable.

You use one or the other, depending on the first letter of the word following the article, for pronunciation reasons. Use a when the next word starts with a consonant, or before words starting in u and eu when they sound like you. Use an when the next word starts with a vowel (a, e, i, o, u) or with a mute h.

Examples :
a boy, an apple, a car, a helicopter, an elephant, a big elephant, an itchy sweater, an ugly duck, a European, a university, a unit, an hour, an honour.

The indefinite article is used to refer to something for the first time or to refer to a particular member of a group or class. Some use cases and examples are given below.

1. Would you like a drink?
2. I’ve finally got a good job.
3. An elephant and a mouse fell into the well.

Example :

1. Mary is training to be an engineer.
2. John is an Englishman
3. I’d like an orange and two lemons please.

Demonstratives
Demonstratives show where an object, event, or person is in relation to the speaker. They can refer to a physical or a psychological closeness or distance. When talking about events, the near demonstratives are often used to refer to the present while the far demonstratives often refer to the past.

Examples:

Possessive Adjectives (Determiners)

Possessive adjectives are not pronouns, but rather determiners. It is useful to learn them at the same time as pronouns, however, because they are similar in form to the possessive pronouns. Possessive adjectives function as adjectives, so they appear before the noun they modify. They do not replace a noun as pronouns do.

Examples :
Did mother find my shoes?
The teacher wants to see your homework.
Samantha will fix her bike tomorrow.
The cat broke its leg.
This is our house.
Where is their school?

Possessive Pronouns

Possessive pronouns replace possessive nouns as either the subject or the object of a clause. Because the noun being replaced doesn’t appear in the sentence, it must be clear from the context.

Examples :
This bag is mine.
Yours is not blue.
That bag looks like his.
These shoes are not hers.
That car is ours.
Theirs is parked in the garage.

Reflexive & Intensive Pronouns

Reflexive and intensive pronouns are the same set of words but they have different functions in a sentence.

Reflexive pronouns refer back to the subject of the clause because the subject of the action is also the direct or indirect object. Only certain types of verbs can be reflexive. You cannot remove a reflexive pronoun from a sentence because the remaining sentence would be grammatically incorrect.

Examples :
I told myself to calm down.
You cut yourself on this nail?
He hurt himself on the stairs.
She found herself in a dangerous part of town.
The cat threw itself under my car!
We blame ourselves for the fire.
The children can take care of themselves.

Quantifiers
Quantifiers are adjectives and adjectival phrases that give approximate or specific answers to the questions “How much?” and “How many?” The pages in this section will teach you more about the different quantifiers in English and how they are used.

• Numbers in English: ordinal, cardinal, and percentages
• To answer the questions How much? and How many? certain quantifiers can be used with countable nouns (friends, cups, people), others with uncountable nouns (sugar, tea, money) and still others with all types of nouns.

Examples :
Would you like some tea and a few cookies?
I always put a little milk and some carrots in my soup.
He has several apples. I don’t have any fruit at all.
She has plenty of clothes for the winter.
I received a large amount of feedback from my survey.

Cardinal Numbers
A Cardinal Number says how many of something there are, such as one, two, three, four, five, etc.
A Cardinal Number answers the question “How Many?”

Examples :
There are twenty children in the class.
He purchased two books.
There are five plates on the table.
Sumitha is fourteen years old.

Ordinal Numbers

An Ordinal Number tells us the position of something in a list, such as first, second, third, fourth, fifth and so on.
Examples :
Let us begin with the first chapter.
We live in the fourth house on the right.
I was bom on the fifteenth of January.
He got the second prize.

Exercises

1. Fill in the blanks with appropriate determiners,
1. Our garden looks awful this summer. There are too ____________ weeds
Answers:
many

2. There aren’t ____________ flowering plants in our garden.
Answers:
many

3. How ____________ pages did you read?
Answers:
many

4. They say ____________ knowledge is a dangerous thing.
Answers:
a little

5. I am having ____________ trouble passing my driving exam.
Answers:
a lot of

6. ____________ people can afford a home these days.
Answers:
few

7. You have ____________ patience
Answers:
little

8. She earns ____________ money than i do
Answers:
less

9. ____________ of the information proved to be outdated.
Answers:
some

10. I didn’t use ____________ fertilizer last spring.
Answers:
much

Choose the correct determiner.
1. There are chairs in this room than in the other room, (more / much)
Answer:
more

2. The assistant didn’t give information, (much / many)
Answer:
much

3. After the negotiations, they made changes in their proposal, (little/few)
Answer:
few

4. mosquitoes appeared after the rain. (A large amount of / A great number of)
Answer:
A great number of

5. Toned Milk has calories than Full Cream Milk, (less / fewer)
Answer:
fewer

6. students taking TOEFL is increasing. (The amount of / The number of)
Answer:
The number of

7. The case had to be reconsidered with new evidence, (these / this)
Answer:
this

8. I like to eat food, (many / a lot of)
Answer:
A lot of

9. She ate French–fries than usual, (fewer / less)
Answer:
fewer

10. He wants to make as money as possible, (much / many)
Answer:
much

11. Vini invited a large of people to the party, (amount/number)
Answer:
number

12. Raji will drink an endless of milk if you let her. (amount / number)
Answer:
Amount

Fill in the blanks with a, an, the, or leave the blank.
1. Han is earning Rupees 1000 _____ hour at the Food court.
Answer:
an

2. Janani makes it ______ habit to buy clothes on sale.
Answer:
a

3. To tell ______ truth, a bank savings account may not be the best place for your money.
Answer:
the

4. Hemá showed initiative when she decided to start a business of her own.
Answer:
an

5. Losing as little as ______ quart of blood can result in shock and unconsciousness.
Answer:
a

6. Over last 20 years, more than 3 million people have visited ______ theme park.
Answer:
the, the

7. Major changes have taken place in ______ Educational services.
Answer:
the

8. Dr. Richards predicts ______ extinction of the whooping crane.
Answer:
th

9. Taking a hot bath is ______ good way to relax.
Answer:
a

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Reported Speech (Direct to Indirect Speech)

Quoting the exact words of the speaker is called “The Direct Speech”.

David said, “I am writing a letter now”.

Reporting of what a speaker said without quoting his exact words is called ‘Indirect Speech’, (also called Reported Speech).

David said that he was writing a letter then.

The following table suggests the words that change during a transformation.

If the reporting verb is in the Present or Future tense (e.g., say, will say) there is no change in the tense of the verb in the Indirect speech.

Anto says, “I eat a mango”. (Direct Speech)
Anto says that he eats a mango”. (Indirect Speech)

If Reporting Verb is in the Past Tense, the tense of the verbs in the reported speech or Indirect Speech must be generally changed.
1. Present Tense in the Direct becomes past tense.
Janis said, “I write a letter”. (D.S)
Janis said that she wrote a letter. (I.S)

2. Past Tense in the Direct becomes past perfect or remains unchanged.
Arun said, “I bought a pen yesterday”. (D.S)
Arun said that he had bought a pen the previous day. (I.S)

3. Present Continuous in the Direct becomes past continuous.
Juber said, “I am going to mosque”. (D.S)
Juber said that he was going to mosque. (I.S)

4. Past Continuous in the Direct becomes past perfect continuous. *
Nelson said, “I was playing cricket”. (D.S) > M
Nelson said that he had been playing cricket. (I.S)

5. Present Perfect in the Direct becomes past perfect.
Kamal said, “I have done my home work”. (D.S)
Kamal said that he had done his home work. (I.S)

6. Present Perfect Continuous in the Direct becomes past perfect continuous.
He said, “I have been reading a novel”. (D.S)
He said that he had been reading a novel. (I.S)

7. ‘Will’ and ‘Shall’ are changed to ‘would’.
He said, “I will go to Trichy tomorrow”. (D.S)
He said that he would go to Trichy the next day. (I.S)

8. may – might
can – could
must – had to (or) must
Nisha said, “I must go now”. (D.S)

Nisha said that she must go then, (or) Nisha said that she had to go then. (I.S)

Hint: Past Perfect and Past Perfect Continuous in the Direct Speech do not take any change *, in their tenses.

Exception to the above rule:
If the direct speech contains the Universal Truth, the tense of the direct speech remains unchanged even if the reporting verb is in the past.

The teacher said, “The sun rises in the East”. (D.S)
The teacher said that the sun rises in the East. (I.S)

Statement (Or) Assertive Sentence

Rules:
Remove the quotation marks in the statement
Use the conjunction ‘that’
Change the reporting verb ‘say to’ into ‘tell’
Change the reporting verb ‘said to’ into ‘told’ ‘

Note: He said that (correct)
He told me that (correct)
He told that (Incorrect)

1. “I will work hard to get first-class” said Nasser (D.S.)
Nasser said that he would work hard to get first class. (I.S.)

2. “You can do this work” said Sundar to Kumar (D.S.)
Sundar told Kumar that he could do that work. (I.S.)

3. He says, “I am glad to be here this evening”(D.S.)
He says that he is glad to be there that evening. (I.S.)

4. “I‘m going to the library now” said David (D.S.)
David said that he was going to the library then. (I.S.)

Imperative Sentence (Order Or Request)

Rules:
Remove the quotation marks in an imperative sentence.
Use ‘to’ if it is an affirmative sentence, (without don’t)
Use ‘not to’ if the sentence is negative, (with don’t)
Don’t use ‘that’
Omit the word ‘please’. Use the word ‘request’ instead of ‘say’.

If the direct speech contains a request or a command, the reporting verb (say, said) change to tell, request, order, command etc. in its correct tense.

1. “Don’t talk in the class” said the teacher to the boys. (D.S.)
The teacher advised the boys not to talk in the class. (I.S.)

2. “Please give me something to eat. I am hungry” the old man said to them. (D.S.)
The old man requested them to give him something to eat and said that he was hungry (I.S.)

3. “Be careful” said he to her. (D.S.)
He warned her to be careful. (I.S.)

4., “Bring me a cup of tea” said Danush to Andrea. (D.S.)
Danush asked Andrea to bring him a cup of tea. (I.S.)

Interrogative Sentence (Questions)

Rules:
Remove the quotation marks and the question mark in the interrogative sentence.
Use ‘if’ or ‘whether’ if the sentence inside the quotation marks begins with a helping verb (Auxiliary verb).
Use the given interrogative word (what, when, where, why, who, whom, whose, which, now etc.) if it does not begin with the helping verb.
Don’t use ‘that’
Changing the reporting verb (say, said) into ‘ask’ or ‘enquire’ in its correct tense.
Omit helping verb like ‘do, does, did’. But don’t omit them when they are with ‘not’.

1. “Won’t you help me to carry this box?” said I to my friend. (D.S.)
I asked my friend if he would not help me to carry that box. (I.S.)

2. Mohan said to Stalin, “Why did not you attend the meeting yesterday”? (D.S.)
Mohan asked Stalin why he had not attended the meeting the day before. (I.S.)

3. “How often do you go to the theatre?” said David to John. (D.S.)
David asked John how often he went to the theatre. (I.S.)

4. Mohamed said to Sultan, “Do you like mangoes?” (D.S.)
Mohamed asked Sultan if he liked mangoes. (I.S.)

Exclamatory Sentence

Rules:
Remove the quotation marks and exclamatory mark.
Change the exclamatory sentence into Statement or Assertive.
Use the conjunction ‘that’.
Omit the interjections such as Oh, O, Alas, how, what, hurrah.
Add the word ‘very’ to the adjective or adverb if necessary.
If the verb is not given, use ‘Be’ form verb (is, was, are, were, am) in its correct tense according to the subject.
Change the reporting verb (say, said) to ‘exclaim joyfully’
Use ‘exclaim’ sorrowfully for sorrowful incidents.

1. “O, what a beautiful flower that is!” said she. (D.S.)
She exclaimed joyfully that that was a very beautiful flower. (I.S.)

2. “What a horrible sight!” we all exclaimed. (D.S.)
We all exclaimed that it was a very horrible sight. (I.S.)

3. “Alas! I have broken my brother’s watch” said he.
He exclaimed sorrowfully that he had broken his brother’s watch. (I.S.)

4. “How beautiful she is!” said Banu. (D.S.)
Banu exclaimed joyfully that she was very beautiful. (I.S.)

Direct Speech Into Indirect Speech

I. Look at the following examples of Direct and Indirect Speech:

1. He said, “Danny will be in London on Tuesday.”
He said that Danny would be in London on Tuesday.

2. “I never eat meat”, he explained.
He explained that he never ate meat.

3. He said, “I wish I knew.”
He said that he wished he knew.

4. She says, “I shall be there.”
She says that she would be there.

5. He said, “She is coming this week.”
He said that she was coming that week.

6. He said, “I bought this pearl for my mother.”
He said that he had bought that pearl for his mother.

7. He said, “Where is she going?”.
He asked where she was going.

8. He said, “Jaya, when is the next bus.”
He asked Jaya when the next bus was.

9. “Is anyone there?” she asked.
She asked if anyone was there.

10. The mother said, “Lie down, David.”
The mother asked David to lie down.

11. He said, “Don’t move, boys.”
He asked the boys not to move.

12. He said, “Please–say nothing about this.”
He asked her to say nothing about that.

Reported Speech–Statement–Rules

Whatever may be the tense of the Reporting Sentence, if the Reported Sentence tells a universal fact, no change is made in the tense of the Reported Sentence.

Example No. 1:
The mother is saying to the child, “The third day of the week is Tuesday. ”.
Step 1 : The Reported Sentence is: The third day of the week is Tuesday.
Step 2 : It is a Statement and a universal fact.
Step 3 : So, the conjunction word is — “that”.
Step 4 : ‘is saying to’ changes into ‘is telling’.
Step 5 : No change of pronoun.
Step 6 : It is a universal fact. So, no change of tense is necessary.
Step 7 : No change of extension.
‘Now, the Indirect Speech is:
The mother is telling the child that the third day of the week is Tuesday.

Example No. 2:
The History teacher says, “Megellan was the first navigator to come around the world. ”.

Step 1 : The Reported Sentence is: “Megellan was the first navigator to come around the world.”
Step 2 : It is a statement.
Step 3 : The conjunction word is — “that”.
Step 4 : ‘Says’ does not change. Use it as it is.
Step 5 : There are no pronouns to get changed.
Step 6 : No change of tense is made.
Step 7 : No extensive word to get changed.

Now, the Indirect Speech is:
The History teacher says that Megellan was the first navigator to come around the world.

Example No. 3:
You know the two types of Interrogative Sentences:
Inverted questions requiring ‘Yes’ or ‘No’ answers — 1st type.
Questions that begin with interrogative words — 2nd type
At first we shall deal with the First type:

Direct Speech: The boy said to the fruit–seller, “Are all these mangoes sweet?”
Step 1 : Identify the Reported Sentence.
Step 2 Know what kind of sentence the Reported Sentence is.
Step 3 Look for the correct Conjunction, (The Conjunction of the First type is “If or Whether”)
Step 4 Change of ‘said to’ — Since it is an interrogative sentence ‘said to ’ changes into ‘asked’.
Step 5 Step Look for the change of pronouns.
Step 6 Look for the change of tenses.

The Reporting Sentence is in past tense. The Reported Sentences is in present tense. So, the Reported Sentence should be changed into past tense, corresponding to the tense, of the Reporting Sentence.

The verb is ‘are’ — Its past tense is ‘were’.

Step 7 : Look for the change of extension words.
‘These’ changes into ‘those’.

The Indirect Speech is : The boy asked the fruit–seller if all those mangoes were sweet.

Example No 4:
Direct Speech: The grandfather said fo his grandsons, “Did you not like my story yesterday?”
SIeR 1 : The Reported Sentence is: “Did you not like my story yesterday?”
Step 2 : ‘It is an interrogative sentence. It is of the First type.
Step 3 : So its conjunction word is: ¡for Whether.
Step 4 : So ‘said to’ changes into ‘asked’.
Step 5 : Look for the pronouns.

(i) The first one is: ‘You’ (subject)
‘You’ — refers to grandsons. They are in the third person plural number.
So the third person of ‘You’ (subject, plural)
It is — ‘they’. ‘You’ changes into ‘they’.
‘You’ — grandsons — ‘They’
‘You’–they.

(ii) The next one is ‘My’.
‘My’ — refers to ‘the grandfather’ — in the third person.
So, take the third person of ‘My’
‘My’ changes into ‘His’.

Step 6 : Look for the change of tenses.
Step 7 : Extensive word ‘Yesterday’ changes into ‘the day before’. Now, the Indirect Speech is-

The grandfather asked his grandsons if they had not liked his story the day before.

Exercises
Transform the following questions into indirect form :

1. Radha asked, “Where are you going?”
Answer:
Radha asked (me) where I was going.

2. Mani asked, “Where are you going to spend the holiday?”
Answer:
Mani asked (me) where I was going to spend the holiday.

3. Jenifer said, “What will you do when you leave school?”
Answer:
Jennifer asked (me) what I would do when I left school.

4. The nurse asked the doctor, “How did you know my name?”
Answer:
The nurse wanted to know how the doctor had known her name.

5. The clerk said, “Do you have an appointment?”
Answer:
The clerk asked (me) whether/if I had an appointment.

6. Bharath said to his wife, “Have you seen my car keys?”
Answer:
Bharath asked his wife whether she had seen his car keys.

7. Rekha’s brother asked her, “Why didn’t you call me?”
Answer:
Rekha’s brother wanted to know why she hadn’t called him.

8. Rayan said to James, “Will you carry my briefcase for me please?”
Answer:
Rayan asked James to carry his briefcase.

9. Charles asked the receptionist, “When can I see the doctor?”
Answer:
Charles asked the receptionist when he could see the doctor.

10. Devi asked, “Where do you live?” ‘
Answer:
Devi asked (me) where I lived.

Change the following sentences into Indirect Speech:

1. He said, “I will do it now.”
Answer:
He said that he would do it then.

2. He says, “Honesty is the best policy.”
Answer:
He says that honesty is the best policy.

3. Ramesh says, “I have written a letter.”
Answer:
Ramesh says that he has written a letter.

4. She said, “Mahesh will be reading a book.”
Answer:
She said that Mahesh would be reading a book.

5. She said, “Where is your father?”
Answer:
She inquired where his father was.

6. He said to me, “Please take your book.”
Answer:
He requested me to take my book.

7. The Principal said to the peon, “Let this boy go out.”
Answer:
The Principal ordered the peon to let that boy go out.

8. He said to me, “May you live long!”
Answer:
He prayed that I might live long.

9. She said, “Goodbye friends!”
Answer:
She bade goodbye to her friends.

10. The student said, “Alas! I wasted my time last year.”
Answer:
The student regretted that he had wasted his time the previous year.

(iii) Change the following sentences into direct speech.

1. She asked me who was the best player..
Answer:
“Who is the best player here?”, she asked.

2. He asked me if I was going home with him.
Answer:
“Are you coming home with me?”, he asked.

3. She asked me what I wanted.
Answer:
She said to me, “What do you want?”.

4. He asked me what the matter was.
Answer:
He said to me, “What is the matter?”.

5. She enquired which her seat was.
Answer:
She said, “Which is my seat?”.

6. I asked whether he did not know the way home.
Answer:
I said, “Don’t you know the way home?”.

7. Aladdin asked the magician what he had done to deserve so severe a blow.
Answer:
Aladdin said to the magician, “What have I done to deserve so severe a blow?”

8. Ulysses asked the little bird whether it had anything to tell him.
Answer:
“Have you anything to tell me, little bird?”, asked Ulysses.

9. He asked me what my name was.
Answer:
He asked me, “What is your name?”.

10. The kind man asked the boy what he could do for him.
Answer:
“What can I do for you?”, the kind man asked the boy.

Students can Download Maths Chapter 3 Geometry Ex 3.1 Questions and Answers, Notes Pdf, Samacheer Kalvi 8th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 2 Chapter 3 Geometry Ex 3.1

Question 1.
Fill in the blanks:

Question (i)
If in a ∆ PQR, PR² = PQ² + QR², then the right angle of ∆ PQR is at the vertex ………
Answer:
Q
Hint:

We have also given Lines and Angles concepts and problems for free of cost on our website.

Question:
(ii) If ‘l’ and ‘m’ are the legs and is the hypotenuse of a right angled triangle then, l² = ……….
Answer:
n² – m²
Hint:

Question (iii)
If the sides of a triangle are in the ratio 5:12:13 then, it is ………
Answer:
a right angled triangle.
13² = 169
5² = 25
12² = 144
169 = 25 + 144
132 = 5² + 12²
By Pythagoras theorem, In a right triangle, square of the hypotenuse is equal to the sum of the squares of other two sides.

Question (iv)
If a perpendicular is drawn to the hypotenuse of a right angled triangle, then each of the three pairs of triangles formed are …………
Answer:
Similar.

Question (v)
In the figure BE² = TE x ………

Answer:
EN

Question 2.
Say True or False.

Question (i)
8, 15, 17 is a Pythagorean triplet.
Answer:
True
Hint:
17² = 289
15² = 225
8² = 64
64 + 225 = 289 ⇒ 17² = 15² + 8²

Question (ii)
In a right angled triangle, the hypotenuse is the greatest side.
Answer:
False
Hint:

Question (iii)
One of the legs of a right angled triangle PQR having ∠R = 90° is PQ.
Answer:
False
Hint:

In ∆ PQR, QR and RP are legs and PQ is the hypotenuse

Question (iv)
The hypotenuse of a right angled triangle whose sides are 9 and 40 is 49.
Answer:
False
Hint:

49² = 2401
9² = 81
40² = 1600
40² + 9² = 1600 + 81 + 1681
49² = 2401
2401 ≠ 1681

Question (v)
Pythagoras theorem is true for all types of triangles.
Answer:
False
Hint:
Pyhtagoras theorem is true for only right angled triangles.

Question 3.
Check whether given sides are the sides of right – angled triangles, using Pythagoras theorem,

1. 8, 15, 17
2. 12, 13, 15
3. 30, 40, 50
4. 9, 40, 41
5. 24, 45, 51

Solution:
1. 8, 15, 17
Take a = 8,
b = 15 and
c = 17
Now a² + b² = 8² + 15² = 64 + 225 = 289
17² = 289 = c²
∴ a² + b² = c²
By the converse of Pythagoras theorem, the triangle with given measures is a right angled triangle.
Answer:
yes.

2. 12, 13, 15
Take a = 12
b = 13 and
c = 15
Now a² + b² = 12² + 13² = 144 + 169 = 313
15² = 225 ≠ 313
By the converse of Pythagoras theorem, the triangle with given measures is not a right angled triangle.
Answer:
No.

3. 30, 40, 50
Take a = 30
b = 40 and
c = 50
Now a² + b² = 30² + 40² = 900 + 1600 = 2500
c² = 50² = 2500
∴ a² + b² = c²
By the converse of Pythagoras theorem, the triangle with given measures is a right angled triangle.
Answer:
yes.

4. 9, 40, 41
Take a = 9
b = 40 and
c = 41
Now a² + b² = 9² + 40² = 81 + 1600= 1681
c² = 41² = 1681
∴ a² + b² = c²
By the converse of Pythagoras theorem, the triangle with given measures is a right angled triangle.
Answer:
Yes.

5. 24, 45, 51
Take a = 24
b = 45 and
c = 51 Now
a² + b² = 24² + 45² = 576 + 2025 = 2601
c² = 51² = 2601
a² + b² = c²
By the converse of Pyhtagoreas theorem, the triangle with given measure is a right angled triangle.
Answer:
Yes.

Question 4.
Find the unknown side in the following triangles.

Solution:
(i) From ∆ ABC, by Pythagoras theorem

BC² = AB² + AC²
Take AB² + AC² = 9² + 40² = 81 + 1600 = 1681
BC² = AB² + AC² = 1681 = 41²
BC² = 41² ⇒ BC = 41
∴ x = 41

(ii) From ∆ PQR, by Pythagoras theorem,

PR² = PQ² + QR²
34² = y² + 30²
⇒ y² = 34² – 30²
= 1156 – 900
= 256 = 16²
y² = 16² ⇒ y = 16

(iii) From ∆ XYZ, by Pythagoras theorem,

YZ² = XY² + XZ²
⇒ XY² = YZ² – XZ²
Z² = 39² – 36²
= 1521 – 1296 = 225 = 15²
Z² = 15²
⇒ Z = 15

Question 5.
An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height.
Solution:
In an isosceles triangle the altitude dives its base into two equal parts. Now in the figure, ∆ ABC is an isosceles triangle with AD as its height.

In the figure, AD is the altitude and Δ ABD is a right triangle.
By Pythagoras theorem,
AB² = AD² + BD²
⇒ AD² = AB² – BD²
= 13² – 12² = 169 – 144 = 25
AD² = 25 = ²
Height: AD = 5 cm

Question 6.
In the figure, find PR and QR.

Solution:
In the figure ∆ PQR is a right triangle.
By Pythagoras theorem,
PR² = PQ² + QR²
(x + 1)² = 7² + x²
x² +2 × x × 1 + 1² = 49+ x²
2x + 1 = 49
2x = 49 – 1 = 48
x = \(\frac{48}{2}\) = 24
∴ PR = x + 1 = 24 + 1 = 25
QR = x = 24

Question 7.
The length and breadth of the screen of an LED – TV are 24 inches and 18 inches. Find the length of its diagonal.

Solution:
The length and breadth of a LED TV form a right angled triangle with its diagonal.
Therefore by Pythagoras theorem,
AC² = AB² + BC²
= 24² + 18² = 576 + 324 = 900 = 30²
∴ AC = 30 ⇒ The length of the diagonal is 30 inches.

Question 8.
Find the distance between the helicopter and the ship.

Solution:
From the figure AS is the distance between the helicopter and the ship.
∆ APS is a right angled triangle, by Pythagoras theorem,
AS² = AP² + PS²
= 80² + 150²
= 6400 + 22500 = 28900 = 170²
∴ The distance between the helicopter and the ship is 170 m

Question 9.
From the figure, 1. If TA = 3 cm and OT = 6 cm, find TG.

Solution:
1. From the figure, if, TA = 3 cm, OT = 6 cm

By Pythagoras theorem,
OA² = OT² – TA² = 6² – 3²
i.e. h² = 36 – 9 = 27 cm.
Now, by altitude – on – hypotenuse theorem
h² = xy
27 = x × 3
x = \(\frac{27}{3}\) = 9 cm
TG = x + 3 = 9 + 3 = 12 cm

Question 10.
If RQ = 15 cm and RP = 20 cm, find PQ, PS and SQ.

Solution:

RQ = 15cm
RP = 20 cm and ∆ PQR is a right angled triangle
By Pythagoras theorem, p 20 cm
PQ² = PR² + RQ² = 20² + 15²
= 400 + 225 = 625 = 25²
∴ PQ = 25 cm
Now by altitude – on – hypotenuse theorem,
RQ² = q x r
15² = q x 25
q = \(\frac{225}{25}\) = 9 cm ⇒ SQ = 9 cm
PR² = P x r
20² = P x 25
P = \(\frac{400}{25}\) = 16 cm ⇒ PS = 16 cm
Answer:

1. PQ = 25 cm
2. PS = 16 cm
3. SQ = 9 cm

Objective Type Questions

Question 11.
If ∆ GUT is isosceles and right angled, then ∠TUG is …………

(a) 30°
(b) 40°
(c) 45°
(d) 55°
Answer:
(c) 45°
Hint:
∠U ∠T = 45° (∆ GUT is an isosceles given)
∴ ∠TUG = 45°

Question 12.
The hypotenuse of a right angled triangle of sides 12 cm and 16 cm is ……….
(a) 28 cm
(b)20cm
(c) 24 cm
(d)21cm
Answer:
(b) 20 cm
Hint:
Side take a = 12 cm
b = 16 cm
The hypotenuse c² = a² + b² = 12² + 16^2
2 = 400 ⇒ c = 20 cm

Question 13.
The area of a rectangle of length 21 cm and diagonal 29 cm is ………. cm²
(a) 609
(b) 580
(c) 420
(d) 210
Answer:
(c) 420
Hint:

Length = 21 cm
Diagonal = 29 cm
By the converse of Pythagoras theorem,
AB² + BC² = AC²
21² + x² = 29²
x² = 841 – 441 = 400 = 20²
x = 20 cm
Now area of the rectangle = length x breadth.
i.e. AB x BC = 21 cm x 20 cm = 420 cm²

Question 14.
if the square of the hypotenuse of an isosceles right triangle is 50 cm2, the length of each side is ………..
(c) 10 cm
(a) 25 cm
(b) 5 cm
(c) 10 cm
(d) 20 cm
Answer:
(b) 5 cm
Hint:
By Pythagoras theorem
c² = a² + b²
In an isosceles triangle, a = b
c² = a² + a² = 2a²
⇒ 2a² = 50
a² = 25 ⇒ a = 5cm
∴ The length of each sides a = 5cm, b = 5 cm.

Question 15.
The sides of a right angled triangle are in the ratio 5 : 12 : 13 and its perimeter is 120 units then, the sides are .
(a) 25, 36, 59
(b) 10, 24, 26
(c) 36, 39, 45
(d) 20, 48, 52
Answer:
(d) 20, 48, 52
Hint:
The sides of a right angled triangle are in the ratio 5 : 12 : 13
Take the three sides as 5a, 12a, 13a
Its perimeter is 5a + 12a + 13a = 30a
It is given that 30a = 120 units
a = 4 units
∴ The sides 5a = 5 x 4 = 20 units
12a = 12 x 4 = 48 units
13a = 13 x 4 = 52 units

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Punctuation

Punctuation refers to the specific markings, signs and symbols that are used in and around sentences to give them structure and to allow for correct understanding and comprehension.

• While writing prose or poetry, we use certain signs to mark the stages of reading. They are called punctuation marks.
• The main purpose of the Punctuation mark is to make the meaning of a sentence clear to the reader.
• Punctuation means the right use of different marks like Full–stop, Comma, Semicolon, Colon, Question Mark…in a written sentence.

Punctuation Marks

1. Full Stop

• Full stop is used to mark the end of a Statement or an Imperative sentence.
  Ex:
  Time is Gold. (Statement)
  Get me a glass of water. (Imperative)
• After an initial (first Letter of a person ‘s name)
  Ex:
  S. Raman
  M. Renu

2. COMMA

• To indicate a pause while reading.
  Ex:
  God willing, we will meet again.
• To separate words in a list. (The last two items are separated by and)
  Ex:
  Health, wealth and peace to together.
  He visited Kerala, Tamil Nadu, Gujarat and Kashmir.
• To separate the actual words spoken, from the rest of the sentences.
  Ex:
  Mala said, “I am writing a letter.”
• To mark off certain words like No, Yes prefixed to a sentence.
  Ex:
  Yes, I come. No, I don’t come.
• To break up group of numbers into tens, hundreds, thousands and lakhs.
  Ex:
  1,25,500
• After salutation in letters.
  Ex:
  Dear Sir, Dear Kannan,
• To separate the date and month from the year.
  Ex:
  1st January, 2005 22nd June, 1969

3. SEMICOLON

• The semicolon represents a pause greater than that indicated by the comma.
  Ex:
  Uma came quickly; she ate in a hurry she went out.
• The comma separates individual items. A semicolon separates groups of items.
  Ex:
  In the children’s room were toys, books, balls and colour pencils; in the kitchen were pots, pans, vegetables, and fruits; and the library had books, charts and maps.

4. COLON

• The colon shows a shorter pause than a full stop, but a longer pause than a semicolon.
  Ex:
  The three great books are: the Ramayana, the Mahabharata and the Gita.
  The days of the week are: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday.

5. APOSTROPHE

• To indicate the omission of a letter or letters when two words are joined.
  Ex:
  I’ve → I have I’m → I am Don’t → Do not won’t → will not
• Apostrophe is used with s– to give the meaning belongs to. (Possessiveness)
  Ex:
  Ramu’s book → The book belongs to Ramu.
• To indicate the plural of figures and letters.
  Ex:
  5’s Your 3’s and 8’s look alike.

6. QUESTION MARK

• To end the interrogative sentence.
  Ex:
  What is your name?
  How old are you?
  Are you interested in Maths?
• To mark off question tag.
  Ex:
  Pass the salt, will you?
  I am not angry, am I?

7. EXCLAMATION MARK

• After interjections.
  Ex:
  Ah! Hurrah! Alas! Oh! Hush!
• After exclamatory phrases.
  Ex:
  Well done! Miserable man!
• After exclamatory sentences.
  Ex:
  What a useful tree the coconut is!
  How cunning the fox is!

8. QUOTATION MARKS

• Single quotation marks or inverted commas are generally used in British English.
  Ex:
  ‘Help! I’m drowning!’
• In American English, double quotation marks are used.
  Ex:
  “Help! I’m drowning!”
• To mark the exact words of a speaker without any change.
  Ex:
  Rama said to Rahim, “Where are you going?”

9. CAPITAL LETTER

• To begin a sentence.
  Ex:
  They are playing cricket.
• To begin each line of poetry.
  Ex:
  If you can dream and not make dreams your master.
  If you can think and not make thoughts your aim.
• For all proper nouns and adjectives derived from them.
  Ex:
  India, Indian.
• To begin the names and surnames of persons, rivers, countries, cities, mountains, roads, buildings, days of the week, months, books, newspapers, magazines, communities, political parties.
  Ex:
  Raj, Cauvery, India, Trichy, Everest, Grand trunk road, The Hindu, Sunday…

10. HYPHEN

• It is used to join up words or syllables.
• To link pairs of words used as single words or group of words.
  Ex:
  home–work, father–in–law, co–operative, two–third.

Exercises
Punctuate the following :
1. On the drive, he would tell me dont waste your time playing insane games with these kids
Answer:
On the drive he would tell me, “Don’t waste your time playing insane games with these kids.

2. “Bow, wow, wow!” wagging his tail violently.
Answer:
“Bow, wow, wow!” wagging his tail violently.

3. Steady old pal weve been through bad things before and come out safely.
Answer:
Steady, old pal! We‘ve been through bad things before and come out safely.

4. do you want to buy it
Answer:
‘Do you want to buy it?’

5. only three years she smiled
Answer:
‘Only three years,’ she smiled.

6. I used to climb the jackfruit tree he said opening his eyes
Answer:
‘I used to climb the jackfruit tree,’ he said, opening his eyes.

7. She said where did you find it
Answer:
She said, “Where did you find it?”

8. A human how could a human be a teacher
Answer:
“A human? How could a human be a teacher?”

9. Oh Jim i’m scared
Answer:
Oh, Jim, I’m scared!

10. she is alive someone said
Answer:
“She is alive!” someone said.

11. Hey wait a minute, ’ pongo shouted.
Answer:
‘Hey! Wait a minute,’ Pongo shouted.

12. tom what on earth ails that cat
Answer:
‘Tom, what on earth ails that cat?’

13. Im a grizzly from alaska and Ive come to stay.
Answer:
“I’m a grizzly from Alaska and I‘ve come to stay.

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Framing Questions

The interrogative pronouns who, what, whom, whose, which and the interrogative Adverbs where, when, why and how are used to frame information questions. The structure ‘how + an adjective/adverb’ may also be used to frame questions.

Exercises
1. John is writing a letter.
Answer:
What is John’s writing?

2. She walks home from school.
Answer:
Who walks home from school?

3. The children are sitting in the garden.
Answer:
Where are the children sitting?

4. Peter runs with his dog on Sundays.
Answer:
When does Peter run with his dog?

5. My rabbit has a cage in the garden.
Answer:
What does your rabbit have in the garden?

6. They go to work by bus.
Answer:
How do they go to work?

7. David likes cats because they are nice.
Answer:
Why does David like cats?

8. Jenny isn’t sleeping late today.
Answer:
Who isn’t sleeping late today?

9. We are going to the cinema.
Answer:
Where are we going?

10. I’m leaving now.
Answer:
When are you leaving?

11. They went to Spain.
Answer:
Where did they go?

12. He writes novels.
Answer:
What does he write?

13. Lacy likes soccer
Answer:
Who likes soccer?

14. The girls watched a serial.
Answer:
What did the girls watch?

15. He discovered the truth.
Answer:
What did he discover?

You can Download Samacheer Kalvi 9th English Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th English Grammar Connectors

Connectors

❖ We could go to the library or the park.
❖ He neither finished his homework nor studied for the test.
❖ I did not go out because the weather was hot.

In each of the above sentences, two different ideas are expressed in one sentence. To connect the ideas, some words like or, neither…nor, because are used. These words and phrases are called Connectors.

A connector may be used to indicate the relationship between the ideas expressed in a clause or a sentence.
The following connectors can be used for different purposes.

Look at the following sentences, how connectors are used.

• The man has much money. However, he isn’t happy at all.
• I like playing football. On the other hand, my brother likes playing basketball.
• His family made a lot of effort to make their son’s lessons better, conversely, he never made any effort.
• She spent four years studying for her law degree. Meanwhile, she continued to work at the bank.
• You are not allowed to use your phone here. Simi Early, you have to switch it off when you are in the library.

Exercises
(i) Choose the best connector.
1. you saved a lot, you wouldn’t be able to buy that bike. (So that, Even if, Therefore)
Answer:
Even if

2. your chances are small, you should try to do it. (Afterwards, Even though, Otherwise)
Answer:
Even though

3. He eats only healthy food his sister gorges herself with junk food. (therefore, because of, whereas)
Answer:
whereas

4. You should learn more, you might fail in your exams. (otherwise, although, because of)
Answer:
otherwise

5. Adhira wanted to play basket ball dance Bharathanatyam. (therefore, even though, as well as)
Answer:
As well as

6. _________ he was very tired, he worked very hard. (Afterwards, So that, Although)
Answer:
Although

7. Slice this meat and _________ you can boil it for thirty minutes. (after wards, although, because of)
Answer:
after wards

8. I cooked dinner _________ my friends wouldn’t have to eat out. (otherwise, unless, so that)
Ans :
so that

9. This street is slippery _________ the snow. (because of, even though, whereas)
Answer:
because of

10. I will pick you up. ________ you can get to the station on time. (Because of, So that, Afterwards)
Answer:
So that

11. Something must be wrong; _________Anu would go to school. (so that, because of, otherwise)
Answer:
otherwise

12. _________ he is very rich, he doesn’t help the poor. (Even if, Although, Therefore)
Answer:
Although

13. _________ the weather was windy, we went for a walk. (Therefore, Otherwise, Even though)
Answer:
Even though

14. She is always helpful and friendly to mc, 1 like her very much. (therefore, whereas, even though)
Answer:
therefore

15. He must be very clever; _________ he wouldn’t have passed such a hard exam. (whereas, otherwise, unless)
Answer:
otherwise

16. _________ I have a bike. I don’t often ride it. (Therefore, Although, Unless)
Answer:
Although

17. I like horror films ________ my friend prefers comedies. (unless, whereas, therefore)
Answer:
he was

18. _________ 1 learned so much, I didn’t manage to pass my exam. (Even though., So that, Because of)
Answer:
Een though

19. You’ll be sick _________ you stop eating so many sweets. (whereas, unless, otherwise)
Answer:
unless
20. _________ we are at the bus station by seven o’clock, we will miss our bus. (Whereas, Unless, Therefore)
Answer:
Unless

(ii) Complete the following with connectors.
1. After he seems quite intelligent _________ he often gets poor grades. (Nonetheless is used to connect two contrasting ideas.)
Answer:
nonetheless

2. This restaurant has some of the best chefs in the town. _________ their service is excellent.
Answer:
Moreover

3. I’ve never been to Kerala ________ having friends and relatives there.
Answer:
in spite of

4. Krishnan is a reckless driver _________ he hasn’t had any accidents.
Answer:
even so

5. My sister works ten hours a day _________ she doesn’t earn much money.
Answer:
however

6. We went out __________ the cold weather.
Answer:
despite

7. 1 tried to look happy _________ feeling ill.
Answer:
ln spite of

8. There is no more food left. _________ there is plenty of snacks.
Answer:
However

9. Wash the potatoes first, _________ you can boil them.
Answer:
After wards

10. I need to work hard _________ I can pass the exam.
Answer:
so that

11. __________ he was the best candidate, he didn’t win the elections.
Answer:
Although

12. _________ you come back from your trip, we’ll meet to discuss the problem.
Answer:
Then

13. They said that the movie was fantastic, _________ I watched it.
Answer:
so

14. _________ he was very ill, he didn’t take any medicine.
Answer:
Although

15. I don’t know ________ I can buy a pair of jeans.
Answer:
where

16. She went to the shops _________ couldn’t find anything that could fit her needs.
Answer:
but

17. Everybody likes him because he is nice _________ helpful.
Answer:
and

18. _________ he was angry with her, he didn’t utter a word.
Answer:
Since

19. Keep quiet _________ go out.
Answer:
or

20. She acted as __________ she is innocent.
Answer:
if

Students can Download Maths Chapter 4 Geometry Ex 4.1 Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 4 Geometry Ex 4.1

Question 1.
Can 30°, 60° and 90° be the angles of a triangle?
Solution:
Given angles 30°, 60° and 90°
Sum of the angles = 30° + 60° + 90° = 180°
∴ The given angles form a triangle.

Question 2.
Can you draw a triangle with 25°, 65° and 80° as angles?
Solution:
Given angle 25°, 65° and 80°.
Sum of the angles = 25° + 65° + 80° = 170° ≠ 180
∴ We cannot draw a triangle with these measures.

Question 3.
In each of the following triangles, find the value of x.

Solution:
(i) Let ∠G = x
By angle sum property we know that,
∠E + ∠F + ∠G = 180°
80° + 55° + x = 180°
135° + x = 180°
x = 45°

(ii) Let ∠M = x
By angle sum property of triangles we have
∠M + ∠M + ∠O = 180°
x + 96° + 22° = 180°
x + 118° = 180°
X = 180° – 118° = 620

(iii) Let ∠Z = (2x + 1)° and ∠Y = 90°
By the sum property of triangles we have
∠x + ∠y + ∠z = 180°
29° + 90° + (2x + 1)° = 180°
119° + (2x + 1)° = 180°
(2x + 1)° = 180° – 119°
2x + 1° = 61°
2x = 61° – 1°
2x = 60°
x = \(\frac{60^{\circ}}{2}\)
x = 30°

(iv) Let ∠J = x and ∠L – 3x.
By angle sum property of triangles we have
∠J + ∠K + ∠L = 180°
x + 112° + 3x = 180°
4x = 180° – 112°
x = 68°
x = \(\frac{68^{\circ}}{4}\)
x = 17°

(v) Let ∠S = 3x°
Given \(\overline{\mathrm{RS}}\) = Given \(\overline{\mathrm{RT}}\) = 4.5 cm
Given ∠S = ∠T = 3x° [∵ Angles opposite to equal sides are equal]
By angle sum property of a triangle we have,
∠R + ∠S + ∠T = 180°
72° + 3x + 3x = 180°
72° + 6x = 180°
x = \(\frac{108^{\circ}}{6}\)
x = 18°

(vi) Given ∠X = 3x; ∠Y = 2x; ∠Z = ∠4x
By angle sum property of a triangle we have
∠X + ∠Y + ∠Z = 180°
3x + 2x + 4x = 180°
∴ 9x = 180°
x = \(\frac{180^{\circ}}{9}\) = 20°

(vii) Given ∠T = (x – 4)°
∠U = 90°
∠V = (3x – 2)°
By angle sum property of a triang we have
∠T + ∠U + ∠V = 180°
(x – 4)° + 90° + (3x – 2)° = 180°
x – 4° + 90° + 3x – 2° = 180°
x + 3x + 90° – 4° – 2° = 180°
4x + 84° = 180°
4x = 180° – 84°
4x = 96°
x = \(\frac{96^{\circ}}{4}\) = 24°
x = 24°

(viii) Given ∠N = (x + 31)°
∠O = (3x – 10)°
∠P = (2x – 3)°
By angle sum property of a triangle we have
∠N + ∠O + ∠P = O
(x + 31)° + (3x – 10)° + (2x – 3)° = 180°
x + 31°+ 3x – 10° + 2x – 3° = 180°
x + 3x + 2x + 31° – 10° – 3° = 180°
6x + 18° = 180°
6x = 180° + 18°
6x = 162°
x = \(\frac{162^{\circ}}{6}\) = 27°
x = 27°

Question 4.
Two line segments \(\overline{A D}\) and \(\overline{B C}\) intersect at O. Joining \(\overline{A B}\) and \(\overline{D C}\) we get two triangles, ∆AOB and ∆DOC as shown in the figure. Find the ∠A and ∠B.

Solution:
In ∆AOB and ∆DOC,
∠AOB = ∠DOC [∵ Vertically opposite angles are equal]
Let ∠AOB = ∠DOC = y
By angle sum property of a triangle we have
∠A + ∠B + ∠AOB = ∠D + ∠C + ∠DOC = 180°
3x + 2x + y = 70° + 30° + y = 180°
5x + y = 100° + y = 180°
Here 5x + y = 100° + y
5x = 100° + y – y
5x = 100°
x = \(\frac{100^{\circ}}{5}\) = 20°
∠A = 3x = 3 × 20 = 60°
∠B = 2x = 2 × 20 = 40°
∠A = 60°
∠B = 40°

Question 5.
Observe the figure and find the value of
∠A + ∠N + ∠G + ∠L + ∠E + ∠S.

Solution:
In the figure we have two triangles namely ∆AGE and ∆NLS.
By angle sum property of triangles,
Sum of angles of ∆AGE = ∠A + ∠G + ∠E = 180° …(1)
Also sum of angles of ∆NLS = ∠N + ∠L + ∠S = 180° … (2)
(1) + (2) ∠A + ∠G + ∠E + ∠N + ∠L + ∠S = 180° + 180°
i.e., ∠A + ∠N + ∠G + ∠L + ∠E + ∠S = 360°

Question 6.
If the three angles of a triangle are in the ratio 3 : 5 : 4, then find them.
Solution:
Given three angles of the triangles are in the ratio 3 : 5 : 4.
Let the three angle be 3x, 5x and 4x.
By angle sum property of a triangle, we have
3x + 5x + 4x = 180°
12x = 180°
x = \(\frac{180^{\circ}}{12}\)
x = 15°
∴ The angle are 3x = 3 × 15° = 45°
5x = 5 × 15° = 75°
4x = 4 × 15° = 60°
Three angles of the triangle are 45°, 75°, 60°

Question 7.
In ∆RST, ∠S is 10° greater than ∠R and ∠T is 5° less than ∠S , find the three angles of the triangle.
Solution:
In ∆RST. Let ∠R = x.
Then given S is ∠10° greater than ∠R
∴ ∠S = x + 10°
Also given ∠T is 5° less then ∠S.
So ∠T = ∠S – 5° = (x + 10)° – 5° = x + 10° – 5°
By angle sum property of triangles, sum of three angles = 180°.

∠R + ∠S + ∠T = 180°
x + x + 10° + x + 5° = 180°
3x + 15° = 180°
3x = 180° – 15°
x = \(\frac{165^{\circ}}{3}\) = 55°
∠R = x = 55°
∠S = x + 10° = 55° + 10° = 65°
∠T = x + 5° = 55° + 5° = 60°
∴ ∠R = 55°
∠S = 65°
∠T = 60°

Question 8.
In ∆ABC , if ∠B is 3 times ∠A and ∠C is 2 times ∠A, then find the angles.
Solution:
In ABC, Let ∠A = x,
then ∠B = 3 times ∠A = 3x
∠C = 2 times ∠A = 2x
By angle sum property of a triangles,
Sum of three angles of ∆ABC =180°.
∠A + ∠B + ∠C = 180
x + 3x + 2x = 180°
x (1 + 3 + 2) = 180°
6x = 180°

x = \(\frac{180^{\circ}}{6}\) = 30°
∠A = x = 30°
∠B = 3x = 3 × 30° = 90°
∠C = 2x = 2 × 30° = 60°
∴ ∠A = 30°
∠B = 90°
∠C = 60°

Question 9.
In ∆XYZ, if ∠X : ∠Z is 5 : 4 and ∠Y = 72°. Find ∠X and ∠Z.
Solution:
Given in ∆XYZ, ∠X : ∠Z = 5 : 4
Let ∠X = 5x; and ∠Z = 4x given ∠Y = 72°
By the angle sum property of triangles sum of three angles of a triangles is 180°.
∠X + ∠Y + ∠Z = 180°
5x + 72 + 4x = 180°
5x + 4x = 180° – 72°
9x = 108°
x = \(\frac{108^{\circ}}{9}\) = 12°
∠X = 5x = 5 × 12° = 60°
∠Z = 4x = 4 × 12° = 48°
∴ ∠X = 60°
∠Z = 48°

Question 10.
In a right angled triangle ABC, ∠B is right angle, ∠A is x + 1 and ∠C is 2x + 5. Find ∠A and ∠C.
Solution:
Given in ∆ABC ∠B = 90°
∠A = x + 1
∠B = 2x + 5

By angle sum property of triangles
Sum of three angles of ∆ABC = 180°
∠A + ∠B + ∠C = 180°
(x + 1) + 90° + (2x + 5) = 180°
x + 2x + 1° + 90° + 5° = 180°
3x + 96° = 180°
3x = 180° – 96° = 84°
x = \(\frac{84^{\circ}}{3}\) = 28°
∠A = x + 1 = 28 + 1 = 29
∠C = 2x + 5 = 2 (28) + 5 = 56 + 5 = 61
∴ ∠A = 29°
∠C = 61°

Question 11.
In a right angled triangle MNO, ∠N = 90°, MO is extended to P. If ∠NOP = 128°, find the other two angles of ∆MNO.
Solution:
Given ∠N = 90°
MO is extended to P, the exterior angle ∠NOP = 128°
Exterior angle is equal to the sum of interior opposite angles.

∴ ∠M + ∠N = 128°
∠M + 90° = 128°
∠M = 128° – 90°
∠M = 38°
By angle sum property of triangles,
∴ ∠M + ∠N + ∠O = 180°
38° + 90° + ∠O = 180°
∠O = 180° – 128°
∠O = 52°
∴ ∠M = 38° and ∠O = 52°

Question 12.
Find the value of x in each of the given triangles.

Solution:
(i) In ∆ABC, given B = 65°,
AC is extended to L, the exterior angle at C, ∠BCL = 135°
Exterior angle is equal to the sum of opposite interior angles.
∠A + ∠B = ∠BCL
∠A + 65° = 135°
∠A = 135° – 65°
∴ ∠A = 70°
x + ∠A = 180° [∵ linear pair]
x + 70° = 180° [∵ ∠A = 70°]
x = 180° – 70°
∴ x = 110°

(ii) In ∆ABC, given B = 3x – 8°
∠XAZ = ∠BAC [∵ vertically opposite angles]
8x + 7 + ∠BAC
i.e., In ∆ABC, ∠A = 8x + 7
Exterior angle ∠XCY = 120°
Exterior angle is equal to the sum of the interior opposite angles.
∠A + ∠B = 120°
8x + 7 + 3x – 8 = 120°
8x + 3x = 120° + 8 – 7
11x = 121°
x = \(\frac{121^{\circ}}{11}\) = 11°

Question 13.
In ∆LMN, MN is extended to O. If ∠MLN = 100 – x, ∠LMN = 2x and ∠LNO = 6x – 5, find the value of x.
Solution:
Exterior angle is equal to the sum of the opposite interior angles.
∠LNO = ∠MLN + ∠LMN

6x – 5 = 100° – x + 2x
6x – 5 + x – 2x = 100°
6x + x – 2x = 100° + 5°
5x = 105°
x = \(\frac{105^{\circ}}{5}\) = 21°
x = 21°

Question 14.
Using the given figure find the value of x.

Solution:
In ∆EDC, side DE is extended to B, to form the exterior angle ∠CEB = x.
We know that the exterior angle is equal to the sum of the opposite interior angles
∠CEB = ∠CDE + ∠ECD
x = 50° + 60°
x = 110°

Question 15.
Using the diagram find the value of x.

Solution:
Given triangle is an equilateral triangle as the three sides are equal. For an equilateral triangle all three angles are equal and is equal to 60° Also exterior angle is equal to sum of opposite interior angles.
x = 60° + 60°.
x = 120°

Objective Type Questions

Question 16.
The angles of a triangle are in the ratio 2:3:4. Then the angles are
(i) 20,30,40
(ii) 40, 60, 80
(iii) 80, 20, 80
(iv) 10, 15, 20
Answer:
(ii) 40, 60, 80

Question 17.
One of the angles of a triangle is 65°. If the difference of the other two angles is 45°, then the two angles are
(i) 85°, 40°
(ii) 70°, 25°
(iii) 80°, 35°
(iv) 80° , 135°
Answer:
(iii) 80°,35°

Question 18.
In the given figure, AB is parallel to CD. Then the value of b is

(i) 112°
(ii) 68°
(iii) 102°
(iv) 62° A
Answer:
(ii) 68°

Question 19.
In the given figure, which of the following statement is true?

(i) x + y + z = 180°
(ii) x + y + z = a + b + c
(iii) x + y + z = 2(a + b + c)
(iv) x + y + z = 3(a + b + c)
Ans :
(iii) x + y + z = 2(a + b + c)]

Question 20.
An exterior angle of a triangle is 70° and two interior opposite angles are equal. Then measure of each of these angle will be
(i) 110°
(ii) 120°
(iii) 35°
(iv) 60°
Answer:
(iii) 35°

Question 21.
In a ∆ABC, AB = AC. The value of x is _____.

(i) 80°
(ii) 100°
(iii) 130°
(iv) 120°
Answer:
(iii) 130°

Question 22.
If an exterior angle of a triangle is 115° and one of the interior opposite angles is 35°, then the other two angles of the triangle are
(i) 45°, 60°
(ii) 65°, 80°
(iii) 65°, 70°
(iv) 115°, 60°
Answer:
(ii) 65°, 80°

Students can Download Maths Chapter 4 Geometry Ex 4.2 Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 4 Geometry Ex 4.2

Question 1.
Given that ∆ABC = ∆DEF (i) List all the corresponding congruent sides
(ii) List all the corresponding congruent angles.
Solution:
Given ∆ABC ≅ DEF.

(i) Corresponding congruent sides.
\(\overline{A B}\) = \(\overline{D E}\); \(\overline{B C}\) = \(\overline{E F}\); \(\overline{A C}\) = \(\overline{D F}\)

(ii) Corresponding congruent angles.
∠ABC = ∠DEF; ∠BCA = ∠EFD ; ∠CAB = ∠FDE

Question 2.
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles.
(i)
(ii)
Solution:
Given ∆PQR ≅ ∆LNM
(i) (a) Corresponding sides
\(\overline{P Q}\) = \(\overline{L N}\) ; \(\overline{P Q}\) = \(\overline{L M}\) ; \(\overline{R Q}\) = \(\overline{M N}\)
(b) Corresponding angles
∠RPQ = ∠NLM; ∠PQR = ∠LNM; ∠PRQ = ∠LMN

(ii) Given ∆PQR ≅ ∆NML
(a) Corresponding angles
\(\overline{Q R}\) = \(\overline{L M}\) ; \(\overline{R P}\) = \(\overline{L N}\); \(\overline{P Q}\) = \(\overline{M N}\)
(b) Corresponding angles
∠PQP = ∠NMN; ∠QRP = ∠MLN; ∠RPQ = ∠LNM

Question 3.
Find the unit digit of expanded form.

(i) ∠A and ∠G
(ii) ∠B and ∠E
(iii) ∠B and ∠G
(iv) \(\overline{A C}\) and \(\overline{G F}\)
(v) \(\overline{B A}\) and \(\overline{F G}\)
(vi) \(\overline{E F}\) and \(\overline{B C}\)
Solution:
Given ∆ABC ≅ ∆EFG. Also from given triangles.
\(\overline{A B}\) = \(\overline{F G}\) \(\overline{B C}\) = \(\overline{G F}\) \(\overline{A C}\) = \(\overline{E F}\)
Also ∠A = ∠F ∠B = ∠G ∠C = ∠E
Answer:
(i) ∠A and ∠G are not corresponding angles.
(ii) ∠B and ∠E are not corresponding angles.
(iii) ∠B and ∠G are corresponding angles.
(iv) \(\overline{A C}\) and \(\overline{G F}\) are not corresponding sides.
(v) \(\overline{B A}\) and \(\overline{F G}\) are corresponding sides.
(vi) \(\overline{E F}\) and \(\overline{B C}\) are not corresponding sides.

Question 4.
State whether the two triangles are congruent or not. Justify your answer.

Solution:
(i) Let the given triangle be ∆ABC. \(\overline{A D}\) divides ∆ABC into two parts giving ∆ABD and ∆ACD.
In ∆ABD and ∆ACD

\(\overline{A B}\) = \(\overline{A C}\) (given)
\(\overline{B D}\) = \(\overline{A D}\) (common side)
∠BAD = ∠CAD (included angles)
∴ By SAS criterion ∆ABD ≅ ∆ACD.

(ii) Let the given triangles in the figure be ∆ABC and ∆DCB.
In both the triangles

\(\overline{B C}\) = \(\overline{B C}\) (Common side)
\(\overline{A B}\) = \(\overline{D C}\)
\(\overline{A C}\) = \(\overline{B D}\)
∴ By SSS Criterion ∆ABC ≅ ∆DCB

(iii) Let the given triangles be ∆ABC and ∆CDE.

Here \(\overline{A C}\) = \(\overline{C E}\) (given)
∠BAC = ∠DEC (given)
∠ACB = ∠DCE (vertically opposite angles)
Two angles and the included side are equal.
Therefore by ASA criterion ∆ABC ≅ ∆CDE.

(iv) Let the two triangles be ∆XYZ and ∆XYW

Here ∠W = ∠Z = 90°
\(\overline{X Y}\) = \(\overline{X Y}\) (Common Hypothenure)
\(\overline{X W}\) = \(\overline{X Z}\) (given)
By RHS criterion ∆XYZ ≅ ∆XYW

(v) Let the two triangles be ∆ABC and ∆ADC

In both the triangles \(\overline{A C}\) = \(\overline{A C}\) (common sides)
\(\overline{A D}\) = \(\overline{B C}\) (given)
\(\overline{A B}\) = \(\overline{D C}\) (given)
By SSS criterion ∆ABC ≅ ∆ADC.

Question 5.
To conclude the congruency of triangles, mark the required information in the following figures with reference to the given congruency criterion.

Solution:
(i) In the given triangles one angle is equal and a side is common and so equal.

To satisfy ASA criterion one more angle should be equal such that the common side is the included side of both angles of a triangle.
The figure will be as follows.

(ii) In the two given triangles two sides of one triangle is equal to two sides of the other triangle.

To satisfy SSS criterion the third sides mut be equal.

(iii) The given triangles have one side in common. They are right angled tringles.

To satisfy RHS criterion their hypotenuse must be equal.

(iv) In the given triangles two angles of one triangle is equal to two angles of the other triangles?

To satisfy ASA criterion included side of two angles must be equal.

(v) In both the triangles one of their sides are equal.

One of their angles are equal or they are vertically opposite angles.
To satisfy SAS criterion, one more side is to be equal such that the angle is the included of the equal sides.

Question 6.
For each pair of triangles state the criterion that can be used to determine the congruency?

Solution:
(i) Given two pair of sides are equal and one side is common to both the triangles.
∴ SSS congruency criterion is used.

(ii) One of the sides and one of the angles are equal.
∴ One more angle is vertically opposite angle and so it is also equal.
ASA criterion is used.

(iii) From the figure hypotenuse and one side are equal in both the triangles.
RHS congruency criterion is used. (∵ Considering ∆ABC and ∆BAD)
∠A = ∠B = 90°
AD = BC
AB = AB (common)
∴ AC = BD (hypotenuse)

(iv) By ASA criterion both triangles are congruent.

(v) By ASA criterion both triangles are congruent. Since two angles in one triangle are equal to two corresponding angles of the other triangle. Again one side is common to both triangle and the side is the included side of the angles.

(vi) Two sides are equal. One angle is vertically opposite angles and one equal.
By SAS criterion both triangles are cogruent.

Question 7.
I. Construct a triangle XYZ with the given conditions.

(i) XY = 6.4 cm, ZY = 7.7 cm and XZ = 5 cm
Solution:


Construction:
Step 1: Draw a line. Marked Y and Z on the line such that YZ 7.7 cm.
Step 2: With Y as centre drawn an arc of radius 6.4 cm above the line YZ.
Step 3: With Z as centre, drwan an arc or radius 5 cm to intersect arc drawn in steps. Marked the point of intersection as X.
Step 3: Joined YX and ZX. Now XYZ is the required triangle.

(ii) An equilateral triangle of side 7.5 cm
Solution:

Construction:
Step 1: Drawn a line. Marked X and Y on the line such that XY = 7.5 cm.
Step 2: With X as centre, drawn an arc of radius 7,5 cm above the line XY.
Step 3: With Y as centre, drawn an arc of radius 7.5 cm to intersect arc drawn in steps. Marked the point of intersection as Z.
Step 4: Joined XZ and YZ. Now XYZ in the required triangle.

(iii) An isosceles triangle with equal sides 4.6 cm and third side 6.5 cm
Solution:

Construction: .
Step 1: Drawn a line. Marked X and Y on the line such that XY = 6.5 cm.
Step 2: With X as centre, drawn an arc of radius 4.6 cm above the line XY
Step 3: with Y as centre, drawn an arc of radius 4.6 cm to intersect arc drawn in steps. Marked the point of intersection as Z.
Step 4: Joined XZ and YZ. Now XYZ is the required triangle.

II. Construct a triangle ABC with given conditions.

(i) AB = 7 cm, AC = 6.5 cm and ∠A = 120°.
Solution:

Construction:
Step 1: Drawn a line. Marked A and B on the line such that AB = 7 cm.
Step 2: At A, drawn a ray AX making an angle of 120° with AB.
Step 3: With A as centre, drawn an arc of radius 6.5 cm to cut the ray AX. Marked the point of intersection as C.
Step 4: Joined BC.
ABC is the required triangle.

(ii) BC = 8 cm, AC = 6 cm and ∠C = 40°.
Solution:


Construction:
Step 1: Drawn a line. Marked B and C on the line such fhat BC = 8 Cm.
Step 2: At C, drawn a ray CY making an angle of 40° with BC.

Step 3: With C as centre, drawn an arc of radius 6 cm to cut the ray CY, marked the point of intersection as A.
Step 4: Joined AB.
AB is the required triangle.

(iii) An isosceles obtuse triangle with equal sides 5 cm
Solution:

Construction:
Step 1: Drawn a line. Marked B and C on the line such that BC = 5 cm.
Step 2: At B drawn a ray BY making on obtuse angle 110° with BC.
Step 3: With B as centre, drawn an arc of radius 5 cm to cut ray BY. Marked the point of intersection as C.
Step 4: Joined BC. ABC is the required triangle.

III. Construct a triangle PQR with given conditions.

(i) ∠P = 60°, ∠R = 35° and PR = 7.8 cm
Solution:

Construction:
Step 1: Drawn a line. Marked P and R on the line such that PR = 7.8 cm.
Step 2: At P, drawn a ray PX making an angle of 60° with PR.
Step 3: At R, drawn another ray RY making an angle of 35° with PR. Mark the point of intersection of the rays PX and RY as Q.
PQR is the required triangle.

(ii) ∠P = 115°, ∠Q = 40° and PQ = 6 cm
Solution:

Construction:
Step 1: Drawn a line. Marked P and Q on the line such that PQ = 6 cm.
Step 2: At P, drawn O ray PX making an angle of 115° with PQ.
Step 3: At Q, drawn another ray QY making an angle of 40° with PQ. Marked the point of intersection of the rays PX and Q Y as R.
PQR is the required triangle.

(iii) ∠Q = 90°, ∠R = 42° and QR = 5.5 cm
Solution:

Construction:
Step 1: Drawn a line. Marked Q and R on the line such that QR = 5.5 cm.
Step 2: At Q, drawn a ray QX making an angle of 90° with QR.
Step 3: At R, drawn another ray RY making an angle of 42° QR. Marked the point of intersection of the rays QX and RY as P.
PQR is the required triangle.

Objective Type Questions

Question 8.
If two plans figures are congruent then they have
(i) same size
(ii) same shape
(iii) same angle
(iv) same shape and same size
Answer:
(iv) same shape and same size

Question 9.
Which of the following methods are used to check the congruence of plane figures?
(i) translation method
(ii) superposition method
(iii) substitution method
(iv) transposition method
Answer:
(ii) superposition method

Question 10.
Which of the following rule is not sufficient to verify the congruency of two triangles.
(i) SSS rule
(ii) SAS rule
(iii) SSA rule
(iv) ASA rule
Answer:
(iii) SSA rule

Question 11.
Two students drew a line segment each. What is the condition for them to be congruent?
(i) They should be drawn with a scale.
(ii) They should be drawn on the same sheet of paper.
(iii) They should have different lengths.
(iv) They should have the same length.
Answer:
(iv) They should have the same length.

Question 12.
In the given figure, AD = CD and AB = CB. Identify the other three pairs that are equal.

(i) ∠ADB = ∠CDB, ∠ABD = ∠CBD, BD = BD
(ii) AD = AB, DC = CB, BD = BD
(iii) AB = CD, AD = BC, BD = BD
(iv) ∠ADB = ∠CDB, ∠ABD = ∠CBD, ∠DAB = ∠DBC
Answer:
(i) ∠ADB = ∠CDB, ∠ABD = ∠CBD, BD = BD

Question 13.
In ∆ABC and ∆PQR, ∠A = 50° = ∠P, PQ = AB, and PR = AC. By which property ∆ABC and ∆PQR are congruent?
(i) SSS property
(ii) SAS property
(iii) ASA property
(iv) RHS property
Answer:
(ii) SAS property

Students can Download Maths Chapter 2 Algebra Intext Questions and Answers, Notes Pdf, Samacheer Kalvi 8th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 2 Chapter 2 Algebra Intext Questions

Exercise 2.1
Try These (Text book page no. 32)

Question 1.
Identify which among the following are linear equations.

1. 2 + x = 19 – Linear as degree of the variable x is 1
2. 7x² – 5 = 3 – not linear as highest degree of x is 2
3. 4p³ = 12 – not linear as highest degree ofp is 3
4. 6m + 2 – Linear, but not an equation
5. n = 10 – Linear equation as degree of n is 1
6. 7k – 12= 0 – Linear equation as degree of Hs 1
7. \(\frac{6x}{8}\) + y = 1 – Linear equation as degree ofx & y is 1
8. 5 + y = 3x – Linear equation as degree ofy & x is 1
9. 10p + 2q = 3 – Linear equation a& degree ofp & q is 1
10. x² – 2x-4 – not linear equation as highest degree of x is 2

Think (Text book page no. 32)

Question 1.
Is t(t – 5)= =10 a linear equation? Why?
Solution:
t(t – 5) = 10
= t x t – 5 x t = 10
= t² – 5t = 10
This is not a linear equation as the highest degree of the variable ‘t’ is 2

Question 2.
Is x² = 2x, a linear equation? Why?
Solution:
x² = 2x
= x² – 2x = 0
This is not a linear equations as the highest degree of the variable ‘x’ is 2

Try These (Text book page no. 33)

Convert the following statements into linear equations:

Question 1.
On subtracting 8 from the product of 5 and a number, I get 32.
Solution:
Convert to linear equations:
Given that on subtracting 8 from product of 5 and a, we get 32
5 × x – 8 = 32
5x – 8 = 32

Question 2.
The sum of three consecutive integers is 78.
Solution:
Sum of 3 consecutive integers is 78
Let 1st integer be ‘x’
∴ x + (x + 1) + (x + 2) = 78
∴ x + x + 1 + x + 2 = 78
3x + 3 = 78

Question 3.
Peter had a Two hundred rupee note. After buying 7 copies of a book he was left with ₹ 60.
Solution:
Let cost of one book be ‘x’
∴ Given that 200 – 7 × x = 60
∴ 200 – 7x = 60

Question 4.
The base angles of an isosceles triangle are equal and the vertex angle measures 80°.
Solution:
Let base angles each be equal to x & vertex bottom angle is 80°. Applying triangle
property, sum of all angles is 180°
∴ x + x + 80 = 180°
2x + 80 = 180°

Question 5.
In a triangle ABC, ∠A is 10° more than ∠B. Also ∠C is three times ∠A. Express the equation in terms of angle B
Solution:
Let ∠B = b
Given ∠A = 10° + ∠B = 10 + b
Also given that ∠C = 3 x ∠A = 3 x (10 + 6) = 30 + 3b
Sum of the angles = 180°
∠A + ∠B + ∠C = 180°
10 + b + b + 30 + 3b = 180°
∴ 5b + 40 = 180°

Think (Text book page no. 34)

Question 1.
Can you get more than one solution for a linear equation?
Solution:
Yes, we can get. Consider the below line or equation
x + y = 5
here, when x = 1, y = 4
when x = 2, y = 2
x = 3, y = 2
x = 4, y = 1
Hence, we get multiple solutions for the same linear equation.

Think (Text book page no. 35)

Question 1.
“An equation is multiplied or divided by a non zero number on either side.” Will there be any change in the solution?
Solution:
Not be any change in the solution

Question 2.
“An equation is multiplied or divided by two different numbers on either side”. What will happen to the equation?
Solution:
When an equation is multiplied or divided by 2 different numbers on either side, there will be a change in the equation & accordingly, solution will also change.

Exercise 2.2
Think (Text book page no. 37)

Question 1.
Suppose we take the second piece to be x and the first piece to be (200 – x), how will the steps vary. Will the answer be different?
Solution:
Let 2nd piece be V & 1st piece is 200 – x
Given that 1st piece is 40 cm smaller than hence the other piece
∴ 200 – x = 2 × x – 40

200 + 40 = 2x + x
240 = 3x
∴ x = \(\frac{240}{3}\) = 80
∴ 1st piece = 200 – x = 200 – 80 = 120 cm
2nd piece = x = 80 cm
The answer will not change

Exercise 2.3
Think (Text book page no. 43)

Question 1.
If instead of (4, 3), we write (3, 4) and try to mark it, will it represent ‘M’ again?
Solution:
Let 3, 4 be M, when we mark, we find that it is a different point and not ‘M’

Try These (Text book page no. 45)

Question 1.
Complete the table given below.

Solution:

Question 2.
Write the coordinates of the points marked in the following figure

• A – (-3, 2)
• B – (5, 2)
• C – (5, -3)
• D – (-3, 3)
• E – (-1,4)
• F – (1, 2)
• G – (7, 4)
• H – (0, 2)
• i – (o, 3)
• J – (-3, 0)
• K – (5, 0)
• L – (-1, 0)
• M – (-2, 0)
• N – (-2, -1)
• O – (0, 0)
• P – (-1, -1)
• Q – (1, -1)
• R – (2, -1)
• S – (0, -3)
• T – (7, 0)
• U – (7, -2)

Exercise 2.4
Think (Text book page no. 49)

Question 1.
Which of the points (5, -10) (0, 5) (5, 20) lie on the straight line X = 5?
Solution:
All points on the line X = 5 will have X – coordinate as 5.
Therefore, any point with X – coordinate as 5 will lie on X = 5 line.
Hence the points (5, – 10) & (5,20) will lie on X = 5

Think (Text book page no. 54)

Question 1.
Why is it given that the speed is ‘constant’? If the speed is not constant, will the graph be the same? The graph is named as y = 80 x algebraically. Why?
Solution:

or in other words, the slope of a line in a distance – time graph. We observe that the slope of the graph is constant hence, speed is constant. If the speed is not constant, the graph will be different as slope of the line would change.

You can Download Samacheer Kalvi 9th Science Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Science Solutions Chapter 16 Applied Chemistry

Samacheer Kalvi 9th Science Applied Chemistry Textbook Exercises

I. Choose the correct answer.

Question 1.
One Nanometre is ………………
(a) 10^{– 7} metre
(b) 10^{– 8} metre
(c) 10^{– 6} metre
(d) 10^{– 9} metre
Answer:
(d) 10^{– 9} metre

Question 2.
The antibiotic Penicillin is obtained from …………………
(a) plant
(b) microorganism
(c) animal
(d) sunlight
Answer:
(b) microorganism

Question 3.
1 % solution of Iodoform is used as ……………..
(a) antipyretic
(b) antimalarial
(c) antiseptic
(d) antacid
Answer:
(c) antiseptic

Question 4.
The cathode of an electrochemical reaction involves …………….
(a) oxidation
(b) reduction
(c) neutralisation
(d) catenation
Answer:
(b) reduction

Question 5.
The age of a dead animal can be determined by using an isotope of ………………..
(a) carbon
(b) iodine
(c) phosphorous
(d) oxygen
Answer:
(a) carbon

Question 6.
Which of the following does not contain natural dyes?
(a) Potato
(b) Beetroot
(c) Carrot
(d) Turmeric
Answer:
(a) Potato

Question 7.
This type of food protect us from deficiency diseases.
(a) Carbohydrates
(b) Vitamins
(c) Proteins
(d) Fats
Answer:
(b) Vitamins

Question 8.
Radiochemistry deals with ……………….
(a) oxidants
(b) batteries
(c) isotopes
(d) nanoparticles
Answer:
(c) isotopes

Question 9.
The groups responsible for the colour of an organic compound is called ………………….
(a) isotopes
(b) auxochrome
(c) chromogen
(d) chromophore
Answer:
(d) chromophore

Question 10.
Chlorinated hydrocarbons are used as ……………..
(a) fertilizers
(b) pesticides
(c) food colourants
(d) preservatives
Answer:
(b) pesticides

II. Fill in the blanks.

1. ……………. is an electrochemical cell which converts electrical energy into chemical change (Reaction).
2. Painkiller drugs are called ……………..
3. Aspirin is an …………….
4. …………. , …………….. and …………… are macronutrients required for plant growth.
5. ……………. is a chemical used in fingerprint analysis.

Answer:

1. Electrolytic cell
2. Analgesic
3. Analgesics
4. Nitrogen, Phosphorous, Potassium
5. Ninhydrin

III. Match the following.

Answer:

1. (c) Fever
2. (e) Electroplating
3. (b) Iodine – 131
4. (a) Large surface area
5. (d) Cancer cell identification

IV. Answer in brief.

Question 1.
What is Chemotherapy?
Answer:
Treatment of certain diseases by destroying the invading organism without damaging the cells of the host, by the use of certain organic compounds is known as Chemotherapy.

Question 2.
What are called Anaesthetics? How are they classified?
Answer:
The drugs which cause loss of sensation are called Anaesthetics.
Types of Anaesthetics

General anaesthetics: They are the agents, which bring about loss of all modalities of sensation, particularly pain along with ‘reversible’ loss of consciousness.
Local anaesthetics: They prevent the pain sensation in localised areas without affecting the degree of consciousness.

Question 3.
What is the need for chemical fertilizers in crop fields?
Answer:
Chemical fertilizers provide the essential micro and macronutrients for crop growth that may not be sufficiently available in the soil.

Question 4.
What is Forensic chemistry related to?
Answer:
Forensic chemistry applies scientific principles, techniques, and methods to the investigation of crime.

V. Answer in detail.

Question 1.
Explain the types of dyes based on their method of application.
Answer:
Dyes are classified in two ways, one, based on the method of application and other on their parent structure.

Based on method of application:

• Acid dyes: These are acidic in nature and used for dyeing animal fibres and synthetic fibres. These can be used for protein fibre such as wool and silk. E.g. Picric acid, Naphthol yellow-s
• Basic dyes: These are basic dyes containing basic group (- NH₂,- NHR, – NR₂). They are used for dyeing animal fibres and plant fibres.
• Mordant dyes or Indirect dyes: These dyes have a poor affinity for cotton fabrics and hence do not dye directly. They require pretreatment of the fibre with a mordant. Mordant (latin: mordere = to bite) is a substance which can be fixed to the fibre and then can be combined with the dye to form an insoluble complex called lake. Aluminium, chromium, and iron salts are widely used as mordants. E.g. alizarin.
• Direct dyes: They have high affinity for cotton, rayon and other cellulose fibre. So they are applied directly as they fix firmly on the fabric. E.g. Congo red
• Vat dyes: It can be used only on cotton and, not on silk and wool. This dyeing is a continuous process and is carried out in a large vessel called vat. So it is called as vat dye. E.g. Indigo

Question 2.
Name various food additives and explain their functions.
Answer:

VI. HOTS

Question 1.
Batteries that are used in mobile phone can be recharged. Likewise, can you recharge the batteries used in watches? Justify your answer.
Answer:
A primary cell cannot be recharged. Watch batteries have a primary cell. In a primary cell, chemical energy is converted into electrical energy when current is drawn from it.

Whereas mobile phones use secondary cells. In secondary cells electrical energy is converted to chemical energy when current is passed through it and chemical energy is converted to electrical energy when current is drawn from it.

Question 2.
Sudha met with a fire accident. What kind of drug(s), she must take?
Answer:
Analgesics are to be administered to reduce the pain followed by antibiotics to prevent infection by microbes.

Question 3.
The soil pH of a cropland is 5. What kind of fertilizers should be used in that land?
Answer:
Organic fertilizer like compost can be used to maintain pH of soil at 6.5, which is ideal for soil and to moderate the acidity.

Samacheer Kalvi 9th Science Applied Chemistry Additional Questions

I. Answer briefly.

Question 1.
Explain the structure of an electrolytic cell.
Answer:

• It is an electrochemical cell which converts electrical energy into chemical energy i.e. in electrolytic cells, electricity is used to bring about chemical reactions.
• Here, both anode and cathode are in contact with Anode same electrolyte and thus the half-cells are not separated. As seen in galvanic cells, electrolytic cell also involves redox reaction. We get electricity from galvanic cells. But electrolytic cells use electricity.
• In electrolytic cells, when electricity is passed to the electrolyte, it dissociates into its constituent ions. These ions undergo redox reaction forming the respective elements. This phenomenon is called Electrolysis. So electrolysis is a process by which an electrolyte is decomposed into its constituent elements by passing electricity through its aqueous solution or fused (molten) state.

Question 2.
How does galvanic cell produce electricity?
Answer:
In a galvanic cell, at anode oxidation takes place which releases electrons. These electrons are attracted by cathode and hence the electrons flowing from anode to cathode are gained in reduction reaction. As long as the redox reaction proceeds, there is a flow of electrons and hence electricity.

Question 3.
What are drugs? What are their characteristics?
Answer:
The chemicals used for treating diseases are termed as drug.
Characteristics of drugs: A drug must possess the following;

1. It should not be toxic
2. It should not cause any side effects.
3. It should not affect the receptor tissue
4. It should not affect the normal physiological activities
5. It should be effective in its action.

Question 4.
Write the applications of Nanochemistry.
Answer:
Some applications of Nanochemistry are:

1. The metallic nanoparticles can be used as very active catalysts.
2. Chemical sensors from nanoparticles and nanowires enhance the sensitivity and sensor selectivity.
3. Nanocoatings and nanocomposites are found useful in making a variety of products such as sports equipment, bicycles and automobiles etc.
4. These are used as novel UV-blocking coatings on glass bottles which protect beverages from being damaged by sunlight.
5. Nanotechnology is being applied in the production of synthetic skin and implant surgery.
6. Nanomaterials that conduct electricity are being used in electronics as minute conductors to produce circuits for microchips.
7. Nanomaterials have extensive applications in the preparation of cosmetics, deodorants and sunscreen lotion and they are used to improve moisturizers without making them too oily.
8. Nanoparticle substances are incorporated in fabrics to prevent the growth of bacteria.
9. Biomedical devices like drug infusion pumps, microneedles and glucometer are made from nanomaterials.
10. Nanochemistry is used in making space, defence and aeronautical devices

Question 5.
What are the applications of Radiochemistry?
Answer:
Important applications of radioisotopes are as under –

• Radiocarbon dating – its a method by which the age of fossil wood or animal is determined using C-14 isotope.
• Study of chemical reactions – the nature of some chemical reactions can be studied by mixing a radioisotope with a non-radioactive isotope of the reactants. The radioisotope used for this purpose is radiotracer.
• Diagnosis – Radioisotope is found very useful to diagnose and understand many diseases.

Question 6.
Write a note on Natural dyes.
Answer:
Many natural dyes have been known from a long time. These are obtained from vegetable sources.

• Henna: It is a reddish-brown dye obtained from plant Lawsonia inermis (Tamil: Maruthondri). A paste of these leaves is used as a hair dye and also for colouring palms.
• Turmeric: It is the traditional natural cosmetic in India. It is obtained from the plant Curcuma. longa. It also acts as an antiseptic. Turmeric is mostly used in India for colouring food.

Question 7.
What is electroplating? Why is it done?
Answer:
The process of depositing a thin layer of one metal over another metal by the process of electrolysis is called electroplating.

It is done to protect the metal from corrosion. For example, metals like iron are electroplated with tin, nickel or chromium to protect from rusting.