Prasanna

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.4

Miscellaneous Practice Problems

Question 1.
The heights (in centimetres) of 40 children are

Prepare a tally mark table.
Solution:

Question 2.
There are 1000 students in a school. Data regarding the mode of transport of the students as given below. Draw a pictograph to represent the data.

Solution:
The pictograph for the mode of transport of students.

Question 3.
The following pictograph shows the total savings of a group of friends in a year. Each picture represents a saving of Rs. 100. Answer the following questions.

(i) What is the ratio of Ruby’s saving to that of Thasnim’s?
(ii) What is the ratio of Kuzhali’s savings to that of others?
(iii) How much is Iniya’s savings?
(iv) Find the total amount of savings of all your friends?
(v) Ruby and Kuzhali save the same amount. Say True or False.
Solution:
(i) Ratio of Ruby’s saving to that of Thasnim’s
\(=\frac{\text { Ruby’s saving }}{\text { Thasnim’s saving }}=\frac{5 \times 100}{4 \times 100}=\frac{5}{4}=5: 4\)
Ratio of Ruby’s saving to that of Thasnims = 5 : 4
(ii) Ratio of Kuzhali’s savings to that of others
\(=\frac{\text { kuzhali’s saving }}{\text { others saving }}=\frac{5 \times 100}{19 \times 100}=\frac{5}{19}=5: 19\)
Ratio of Kuzhali’s saving to that of others = 5 : 19
(iii) Iniya’s saving = 3 × 100 = ₹ 300
(iv) Saving of all the friends = (5 + 7 + 4 + 5 + 3) × 100 = 24 × 100 = ₹ 2400.
Total savings = ₹ 2400
(v) True.

Challenging Problems

Question 4.
The table shows the number of moons that orbit each of the planets in our solar system.

Make a Bar graph for the above data.
Solution:

Question 5.
The predictions of Weather in the month of September is given below:

(i) Make a frequency table of the types of weather by reading the calender.
(ii) How many days are either cloudy or partly cloudy
(iii) How many days do not have rain? Give two ways to find the answer?
(iv) Find the ratio of the number of sunny days to Rainy days.
Solution:
Frequency Table for the Type of weather for the month of September

(ii) 14 days.
(iii) For 24 days there is no rain.
(a) From the total 30 days, we subtract the rainy days i.e 30 – 6 = 24 days (from the frequency table)
(b) From the picture, we can count the non-rainy days.
(iv) Ratio of number of Sunny day to Rainy days
\(=\frac{\text { Number of Sunny days }}{\text { Number of Rainy days }}=\frac{10}{6}=\frac{5}{3}=5: 3\)
The ratio of a number of Sunny days to Rainy days = 5 : 3.

Question 6.
26 students were interviewed to find out what they want to become in future. Their responses are given in the following table.

Represent this data using the pictograph
Solution:

Question 7.
Yasmin of class VI was given a task to count the number of books which are biographies, in her school library. The information collected by her is represented as follows.

Observe the pictograph and answer the following questions.
(i) Which title has the maximum number of biographies?
(ii) Which title has the minimum number of biographies?
(iii) Which title has exactly half the number of biographies as Novelists?
(iv) How many biographies are there on the title of Sportspersons?
(v) What is the total number of biographies in the library?
Solution:
(i) ‘The title Novelists’ have the maximum number of biographies
(ii) ‘The title Scientists’ have the minimum number of biographies.
(iii) ‘Sportspersons’ title has exactly half the number of biographies as Novelist.
(iv) \((1 \times 20)+\frac{20}{4}=20+5=25\) biographies are there in the title sportsperson.
(v) 8 × 20 = 160 biographies are there in the library.

Question 8.
The bar graph illustrates the results of a survey conducted on vehicles crossing over a Toll Plaza in on hour.

Observe the bar graph carefully and fill up the following table.

Solution:

Question 9.
The lengths (in the nearest centimetre) of 30 drumsticks are given as follows.

Draw the bar graph showing the same information.
Solution:
The bar graph showing the same information is given below:

Question 10.
Given two angles are supplementary i.e. their sum = 180°.
Solution:
Let the angle be x.
Then anothcf angle = x + 20 (given)

The two angles are 80° and 100°

Students can Download Maths Chapter 1 Number System Ex 1.2 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 1 Chapter 1 Number System Ex 1.2

Question 1.
Fill in the blanks
(i) -44 + ____ = -88
(ii) ___ – 75 = -45
(iii) ___ – (+50) = -80
Solution:
(i) -44
(ii) 30
(iii) -30

Question 2.
Say True or False.
(i) (-675) – (-400) = -1075
(ii) 15 – (-18) is the same as 15 + 18
(iii) (-45) – (-8) = (-8) – (-45)
Solution:
(i) False
(ii) True
(iii) False

Question 3.
Find the value of the following.
(i) -3 – (-4) using number line.
Solution:
We start at zero facing positive direction. Move 3 units backward to represent (-3). Then turn towards the negative side and move 4 units backwards. We reach+1.

∴ (-3) – (-4) = +1

(ii) 7 – (-10) using number line
Solution:

We start at zero facing positive direction. Move 7 units forward to represent (+7). Then turn towards the negative side and move 10 units backwards.
We reach +17
∴ 1 – (-10) = +17

(iii) 35 – (-64)
Solution:
35 – (-64) = 35+ (Additive inverse of-64) = 35 + (+64) = 99
∴ 35 – (-64) = 99

(iv) -200 – (+100)
Solution:
-200 – (+100) = -200 + (Additive inverse of+100) = -200 + (-100) = -300
-200 – (+100) = -300

Question 4.
Kabilan was having 10 pencils with him. He gave 2 pencils to senthil and 3 to Karthick. Next day his father gave him 6 more pencils, from that he gave 8 to his sister. How many pencils are left with him?
Solution:
Total pencils Kabilan had = 10
No. of pencils given to Senthil = 2
No. of pencils given to Karthick = 3.
Now number of pencils left with Kabilan = 10 – 2 – 3 = 8 – 3 = 5
Number of pencils got from his father = 6
No. total pencils Kabilan had = 5 + 6 = 11
Number of pencils given to his sister = 8
Number of pencils left with Kabilan = 11 – 8 = 3

Question 5.
A lift is on the ground floor. If it goes 5 floors down and then moves up to 10 floors from there, then in which floor will the lift be?
Solution:
Initially the lift will be in the ground floor representing ‘0’
It goes to 5 floors down ⇒ -5
Then it moves 10 floors up +10.
Now the lift will be = 0 – 5 + 10 = -5 + 10
= 5^th floor (above the ground floor)

Question 6.
When Kala woke up, her body temperature was 102°F. She took medicine for fever. After 2 hours it was 2°F lower. What was her temperature then?
Solution:
Kala’s temperature initially = 102°F
After two hours the temperature decreased = -2°F
Now the final temperature = 102°F – 2°F = 100°F

Question 7.
What number should be added to (-17) to get -19?
Solution:
According to the problem = -17 + A number = -19
The number = -19 + 17 = -2
∴ -2 should be added to -17 to get -19

Question 8.
A student was asked to subtract (-12) from -47. He got -30. Is he correct? Justify.
Solution:
Subtracting -12 from -47, we get
-47 – (-12) = -47 + (Additive inverse of-12)
= -47 + (+12) = -35
But the students answer is -30.
So he is not correct.

Objective Type Questions

Question 9.
(-5) – (-18)
(i) 23
(ii) -13
(iii) 13
(iv) -23
Solution:
(iii) 131

Question 10.
(-100) – 0 + 100 =
(i) 200
(ii) 0
(iii) 100
(iv)-200
Solution:
(ii) 0

Students can Download Maths Chapter 1 Number System Ex 1.4 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 1 Chapter 1 Number System Ex 1.4

Question 1.
Fill in the blanks.
(i) (-40) ÷ ___ =40
(ii) 25 ÷ ____ = -5
(iii) ____ ÷ (-4) = 9
(iv) (-62) ÷ (-62) = ____
Solution:
(i) -1
(ii) -5
(iii) -36
(iv) 1

Question 2.
Say True or False:
(i) (-30) ÷ (-6) = -6
(ii) (-64) ÷ (-64) is 0
Solution:
(i) False
(ii) False

Question 3.
Find the values of the following.
(i) (-75) ÷ 5
(ii) (-100) ÷ (-20)
(iii) 45 ÷ (-9)
(iv) (-82) ÷ 82
Solution:
(i) \(\frac{-75}{5}\) = -15
(ii) \(\frac{-100}{-20}\) = 5
(iii) \(\frac{45}{-9}\) = -5
(iv) \(\frac{-82}{82}\) = -1

Question 4.
The product of two integers is -135. If one number is -15. Find the other integer.
Solution:
Given the product of two integers = -135
One of them = -15
∴ -15 × Another number = -135
Other number = \(\frac{-135}{-15}\) = 9
∴ The other number = 9.

Question 5.
In 8 hours duration, with uniform decrease in temperature, the temperature dropped 24°C. How many degrees did the temperature drop each hour?
Solution:
In 8 hours the drop in temperature = 24
In 1 hour the drop in temperature = \(\frac{24}{8}\) = 3°
The temperature dropped 3°C every hour.

Question 6.
An elevator descends into a mine shaft at the rate of 5 m/min. If the descent starts from 15 m above the ground level, how long will it take to reach -250 m?
Solution:
The elevator’s position = 15 m above ground level = +15 m
It should reach = -250 m
The distance to be travelled = 15 – (-250) m = 15 + (+250) m 265 m
Time taken to descend 5 m = 1 min
∴ Time required to descend 265 m = \(\frac{24}{8}\) = 53 min

Question 7.
A person lost 4800 calories in 30 days. If the calory loss is uniform, calculate the loss of calory per day.
Solution:
Loss of calory in 30 days = 4800
∴ Loss of calory in 1 day = \(\frac{4800}{30}\) = 160 calories
∴ 160 calories lost per day.

Question 8.
Given 168 × 32 = 5376 then fined (-5376) ÷ (-32).
Solution:
Given 168 × 32 = 5376
∴ \(\frac{5376}{32}\) = 168
Also, \(\frac{-5376}{-32}\) = 168

Question 9.
How many -4’s are there is (-20)?
Solution:
Number of -4’s in (-20) = \(\frac{-20}{-4}\) = 5

Question 10.
(-400) divided into 10 equal parts gives ____
Solution:
\(\frac{-400}{10}\) = -4

Objective Type Questions

Question 11.
Which of the following does not represent an integer?
(i) 0 ÷ (-7)
(ii) 20 ÷ (-4)
(iii) (-9) ÷ 3
(iv) 12 ÷ 5
Solution:
(iv) 12 ÷ 5

Question 12.
(-16) ÷ 4 is the same as
(i) -(-16 ÷ -4)
(ii) -(16) ÷ (-4)
(iii) 16 ÷ (-4)
(iv) -4 ÷ -16
Solution:
(iii) 16 ÷ (-4)

Question 13.
(-200) ÷ 10 is
(i) 20
(ii) -20
(iii) -190
(iv) 210
Solution:
(ii) 20

Question 14.
The set of integers is not closed under
(i) Addition
(ii) Subtraction
(iii) Multiplication
(iv) Division
Solution:
(iv) Division

Students can Download Maths Chapter 6 Information Processing Ex 6.2 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 1 Chapter 6 Information Processing Ex 6.2

Miscellaneous Practice Problems

Question 1.
Make a model of a fish using the given tetromino shapes

Complete the given rectangle using the given tetromino shapes.
Solution:

Question 2.
Complete the given rectangle using the given tetromino shapes.

Solution:

Question 3.
Shade the figure completely, by using five Tetromino shapes only once.

Solution:

Question 4.
Using the given tetrominoes with numbers on it complete the 4 × 4 magic square?

Solution:

Question 5.
Find the shortest route to Vivekanandar Memorial Hall from the Mandapam using the given map.

Solution:
Possible routes from Mandapam to Vivekandar Memorial are

route 1:
(a) Mandapam ➝ Pullivasal Island ➝ Krusadai Island ➝ Vivekanandar Memorial Hall.
Distance = 6 Km + 2 Km + 1.5 Km = 9.5 Km

route 2:
(b) Mandapam ➝ Krusadai Island ➝ Vivekanandar Memorial Hall.
Distance = 7 Km + 1.5 Km = 8.5 Km
8.5 km < 9.5 km
∴ Shortest route : Mandapam ➝ Krusadai Island ➝ Vivekanandar Memorial Hall.

Challenge Problems

Question 6.
Fill in 4 × 10 rectangle completely, using all the five tetrominoes twice.
Solution:

(more possible ways are there)

Question 7.
Fill in 8 × 5 rectangle completely, using all the five tetrominoes twice.
Solution:

(more possible way are there)

Question 8.
Observe the picture and answer the following.
(i) Find all the possible routes from A to D.
(ii) Find the shortest distance between E and C.
(iii) Find all the possible routes between B and F with distance. Mention the shortest route.

Solution:
(i) All possible routes from A to D are :
(a) A ➝ G ➝ F ➝ E ➝ D
(b) A ➝ G ➝ D
(c) A ➝ B ➝ C ➝ D
(d) A ➝ B ➝ D

(ii) Distance between E and C are
(a) Route 1: E ➝ D ➝ C
Distance: 120 m + 200 m = 320 m.
(b) Route 2: E ➝ D ➝ B ➝ C
Distance = 120 + 100 m + 120 m
= 340 m.
∴ Shortest distance is 320 m.

(iii) All possible routes between B and F are :
(a) Route 1: B ➝ A ➝ G ➝ F
Distance = 250 m + 100 m + 150 m = 600 m.

(b) Route 2: 2 ➝ D ➝ E ➝ F
Distance = 100 m + 120 m + 300 m
= 520 m.

(c) Route 3: B ➝ D ➝ G ➝ F
Distance = 100 m + 200 m + 150 m
= 450 m.

(d) Route 4: B ➝ C ➝ D ➝ E ➝ F
Distance = 120 m + 200 m + 120 m + 300 m
= 740 m.
We find that Route 3 is shortest.
ie B ➝ D ➝ G ➝ F is the shortest route.

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Additional Questions

Question 1.
A _____ is a collection of numbers gathered to give some meaningful information.
Solution:
Data

Question 2.
The data can be arranged in a tabular form using ____ marks
Solution:
Tally

Question 3.
A observation occurring 8 times in a data is represented as _____ using tally marks.
Solution:

Question 4.
Tally marks  represents _____
Solution:
6

Question 5.
Following are the choice of sports for 20 students of class VI.

Arrange the names of sports in a table using tally marks.
Solution:

Question 6.
Mariana threw a die 40 times and noted the number appearing each time as shown below.

Make a table and enter the data using tally marks.
Find the number that appeared
(a) the minimum number of times
(b) the maximum number of times
(c) Find those numbers that appear an equal number of times.
Solution:
Table using Tally Marks

(a) The number ‘4’ appeared the minimum number of times
(b) The number ‘5’ appeared the maximum number of times
(c) Numbers ‘1’ and ‘6’ appeared the equal number of times.

Question 7.
What is the advantage of using pictograph?
Solution:
The data can be analyzed and interpreted. The pictures and symbols help us to understand better.

Question 8.
Total number of students of a school in different years is shown in the following table

(A) Prepare a pictograph of students using one symbol to represent 100 students and answer the following questions
(a) How many symbols represent the total number of students in the year 2000?
(b) How many symbols represent the total number of students in the year 1997?
Solution:
(A) The pictograph is given by

(a) 9 Full pictures and a half picture represent the number of students in the year 2000
(b) 5 symbols.

Question 9.
The number of bottles of honey sold by three different shops are given below.

(A) Draw a pictograph and answer the following questions (use the scale – 20 bottles)
(a) What is the total profit of shop A, if the profit gained on each bottle is ‘E’150?
(b) If the total number of bottles sold is 400 how many figures must be drawn to shops?
(c) Find the difference between the number of bottles sold by shop B and the number of bottles sold by shop ‘C’.
Solution:
(A) Pictograph of number of bottles sold

(a) Profit per bottle = ₹ 150
Shop A’s total profit = 80 × 150 = ₹ 12,000
(b) For 400 bottles, the figures to be drawn is \(\frac{400}{20}\) = 20 bottles for shop ‘C ’
(c) Difference = No. of bottles sold by shop ‘C’ – No. of bottles sold by shop ‘B’ = 180 – 140 = 40 bottles

Question 10.
The following data is the total savings of a group of 5 friends in a year.

Draw a pictograph to represent the data.
Solution:

Question 11.
The number of mathematics books sold by a shopkeeper on six consecutive days is shown below.

Draw a bar graph to represent the above information choosing the scale of your choice.
Solution:

Question 12.
The following bar graph shows the number of people visited Mahabalipuram over a period of 5 months.

Use the graph to answer the following questions
(a) How many people visited Mahabalipuram in April?
(b) How many more people visited Mahabalipuram in May than in January?
(c) In which month, were there as many visitors as in March?
(d) In which month was there 1500 more visitors than in January?
(e) How many visitors were there in 5 months?
Solution:
(a) 3500 people visited Mahabalipuram in April
(b) 500 more people
(c) January
(d) April
(e) 11,500 people

Students can Download Maths Chapter 4 Geometry Additional 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 1 Chapter 4 Geometry Additional Questions

Additional Questions And Answers

Very Short Answers [2 Marks]

Question 1.
In the given figure if ∠A = ∠C then prove that ∆AOB ~ ∆COD.

Solution:
In triangles ∆AOB and ∆COD
∠A = ∠C (Y given)
∠AOB = ∠COD [∵ Vertically opposite angles]
∠ABO = ∠CDO [Remaining angles of ∆AOB and ∆COD]
∴ ∆AOB ~ ∆COD [∵ AAA similarity]
∵ ∆AOB ~ ∆COD [∵ AAA similarity]

Question 2.
In the figure AB ⊥ BC and DE ⊥ AC prove that ∆ABC ~ ∆AED.

Solution:
In triangles ∆ABC and ∆AED
∠ABC = ∠AED = 90°
∠BAC = ∠EAD [Each equal to A]
∠ADE = ∠ACB [∵ Remaining angles]
∴ By AAA criteria of similarity ∆ABC ~ ∆AED

Short Answers [3 Marks]

Question 1.
In the figure with respect to ABEP and CPD prove that BP × PD = EP × PC.

Solution:
Proof:
In ∆EPB and ∆DPC
∠PEB = ∠PDC = 90° [given]
∠EPB = ∠DPC [Vertically opposite angles]
∠EPB = ∠PCD [∵ Remaining angles]
Thus,

Long Answers [5 Marks]

Question 1.
P and Q are points on sides AB and AC respectively of ∆ABC. If AP = 3 cm PB = 6cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.
Solution:

AB = AP + PB
= 3 + 6 cm = 9 cm
AC = AQ + QC = 510 cm = 15

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Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 4 Geometry Additional Questions

Construct the quadrilaterals with the following measurements and also find their area.

Question 1.
ABCD, AB = 5 cm, BC 4.5 cm, CD = 3.8 cm, DA = 4.4 cm and AC = 6.2 cm.
Solution:
Given AB = 5 cm,
BC = 4.5 cm,
CD = 3.8 cm,
DA = 4.4 cm,
AC = 6.2 cm

Steps:
1. Draw a line segment AB = 5 cm
2. With A and B as centers drawn arcs of radii 6.2 cm and 4.5cm respectively and let them cut at C.
3. Joined AC and BC.
4. With A and C as centrers drawn arcs of radii 4.4cm and 3.8 cm respectively and let them at D.
5. Joined AD and CD.
6. ABCD is the required quadrilateral.
Calculation of Area:

Question 2.
KITE, KI = 5.4 cm, IT = 4.6 cm, TE= 4.5 cm, KE = 4.8 cm and IE = 6 cm.
Solution:
Given, KI = 5.4 cm,
IT = 4.6 cm,
TE= 4.5 cm,
KE = 4.8 cm,
IE = 6 cm.

Steps:
1. Draw a line segment KI = 5.4 cm
2. With K and I as centers drawn arcs of radii 4.8 cm and 6 cm respectively and let them cut at E.
3. Joined KE and IE.
4. With E and I as centers, drawn arcs of radius 4.5cm and 4.6 cm respectively and let them cut at T.
5. Joined ET and IT.
6. KITE is the required quadrilateral.
Calculation of Area:

Question 3.
PLAY, PL = 7 cm, LA = 6 cm, AY= 6 cm, PA = 8 cm and LY = 7 cm.
Solution:
Given PL = 7 cm,
LA = 6 cm,
AY= 6 cm,
PA = 8 cm,
LY = 7 cm

Steps:
1. Draw a line segment PL = 7 cm
2. With P and L as centers, drawn arcs of radii 8 cm and 6 cm respectively, let them cut at A.
3. Joined PA and LA.
4. With L and A as centers, drawn arcs of radii 7 cm and 6 cm respectively and let them cut at Y.
5. Joined LY, PY and AY.
6. PLAY is the required quadrilateral.
Calculation of Area:

Question 4.
LIKE, LI = 4.2 cm, IK = 7 cm, KE = 5 cm, LK = 6 cm and IE = 8 cm.
Solution:
LI = 4.2 cm,
IK = 7 cm,
KE = 5 cm,
LK = 6 cm,
IE = 8 cm

Steps:
1. Draw a line segment LI = 4.2 cm
2. With L and I as centers, drawn arcs of radii 6 cm and 7 cm respectively and let them cut at K.
3. Joined LK and IK.
4. With I and K as centers, drawn arcs of radius 8 cm and 5 cm respectively and let them cut at E.
5. Joined LE, IE and KE.
6. LIKE is the required quadrilateral.
Calculation of Area:

Question 5.
PQRS, PQ = QR = 3.5 cm, RS = 5.2 cm, SP = 5.3 cm and ∠Q =120° .
Solution:
PQ = QR = 3.5 cm,
RS = 5.2 cm,
SP = 5.3 cm ,
∠Q =120°

Steps:
1. Draw a line segment PQ = 3.5 cm
2. Made ∠Q = 120°. Drawn the ray QX.
3. With Q as centre drawn an arc of radius 3.5 cm. Let it cut the ray QX at R.
4. With R and P as centres drawn arcs of radii 5.2cm and 5.5 cm respectively and let them cut at S.
5. Joined PS and RS.
6. PQRS is the required quadrilateral.
Calculation of Area:
Area of the quadrilateral PQRS = 18 cm²

Question 6.
EASY, EA = 6 cm, AS = 4 cm, SY = 5 cm, EY = 4.5 cm and ∠E = 90°.
Solution:
EA = 6 cm,
AS = 4 cm,
SY = 5 cm,
EY = 4.5 cm,
∠E = 90°

1. Drawn a line segment EA = 6 cm
2. Made ∠E = 90°. From E drawn the ray EX.
3. With E as center drawn an arc of 4.5 cm radius. Let of cut the ray EX at Y.
4. With A and Y as centres drawn arcs of radii 4 cm and 5 cm respectively and let them cut at S.
5. Joined AS and YS.
6. EASY is the required quadrilateral.
Calculation of Area:

∴ Area of the quadrilateral = 22.87 cm²

Question 7.
MIND, MI = 3.6 cm, ND = 4 cm, MD = 4 cm, ∠M = 50° and ∠D = 100°.
Solution:
MI = 3.6 cm,
ND = 4 cm,
MD= 4 cm,
∠M = 50°,
∠D = 100°

1. Draw a line segment MI = 3.6 cm
2. At M on MI made an angle ∠IMX = 50°
3. Drawn an arc with center M and radius 4 cm let it cut MX it D
4. At D on DM made an angle ∠MDY = 100°
5. With I as center drawn an arc of radius 4 cm, let it cut DY at N.
6. Joined DN and IN.
7. MIND is the required quadrilateral.
Calculation of Area:

Area of the quadrilateral = 9.6 cm²

Question 8.
WORK, WO = 9 cm, OR = 6 cm, RK = 5 cm, ∠O = 100° and ∠R = 60°.
Solution:
WO = 9 cm,
OR = 6 cm,
RK = 5 cm,
∠O = 100°,
∠R = 60°

Steps:
1. Drawn a line segment WO = 9 cm
2. At O on WO made an angle ∠WOR = 100° and drawn the ray OX.
3. Drawn an arc of radius 6 cm with center O. Let it intersect OX at R.
4. At R on OR, made ∠ORY = 60°, and drawn the ray RY.
5. With center R drawn an arc of radius 5 cm, let it intersect RY at K.
6. Joined WK.
7. WORK is the required quadrilateral.
Calculation of Area:

Area of the quadrilateral = 31.59 cm²

Question 9.
AGRI, AG = 4.5 cm, GR = 3.8 cm, ∠A = 90°, ∠G = 110° and ∠R = 90°.
Solution:
AG = 4.5 cm,
GR = 3.8 cm,
∠A = 90°,
∠G = 110°,
∠R = 90°

1. Draw a line segment AG = 4.5 cm
2. At G on AG made ∠AGX =110°
3. With G as centre drawn an arc of radius 3.8 cm let it cut GX at R.
4. At R on GR made ∠GRZ = 90°
5. At A on AG made ∠GAY = 90°
6. AY and RZ meet at I.
7. AGRI is the required quadrilateral.
Calculation of Area:

Question 10.
YOGA, YO = 6 cm, OG = 6 cm, ∠O = 55°, ∠G = 55° and ∠A = 55°.
Solution:
YO = 6 cm,
OG = 6 cm,
∠O = 55°,
∠G = 55°,
∠A = 55°

Steps:
1. Draw a line segment OG = 6 cm
2. At G on DG made an angle ∠OGY = 55°
3. AT G on GO made ∠GOX = 55°.
4. GY and OX meet cut A.
5. At A on OA made ∠OAZ = 55°
6. Drawn an arc of radius 6 cm with center O. It cut AZ at Y. Joined OY.
7. YOGA is the required quadrilateral.
Calculation of Area:

Area of the quadrilateral YOGA = 28.08 cm²

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 3 Ratio and Proportion Intext Questions

Recap (Textbook Page No. 55)

Question 1.
Which of the following fractions is not a proper fraction?
(a) \(\frac{1}{3}\)
(b) \(\frac{2}{3}\)
(c) \(\frac{5}{10}\)
(d) \(\frac{10}{5}\)
Solution:
(d) \(\frac{10}{5}\)

Question 2.
The equivalent fraction of \(\frac{1}{7}\) is ____
(a) \(\frac{2}{15}\)
(b) \(\frac{1}{49}\)
(c) \(\frac{7}{49}\)
(d) \(\frac{100}{7}\)
Solution:
(c) \(\frac{7}{49}\)

Question 3.
Write >, < or = in the box.
(i) \(\frac{5}{8}\) ____ \(\frac{1}{10}\)
(ii) \(\frac{9}{12}\) _____ \(\frac{3}{4}\)
Solution:

Question 4.
Arrange these fractions from the least to the greatest: \(\frac{1}{2}, \frac{1}{4}, \frac{6}{8}, \frac{1}{8}\)
Solution:
\(\begin{array}{l}{\frac{1}{2}=\frac{1 \times 4}{2 \times 4}=\frac{4}{8}} \\ {\frac{1}{4}=\frac{1 \times 2}{4 \times 2}=\frac{2}{8}}\end{array}\)
Comparing \(\frac{4}{8}, \frac{2}{8}, \frac{6}{8} \text { and } \frac{1}{8}\). we have \(\frac{1}{8}<\frac{2}{8}<\frac{4}{8}<\frac{6}{8}\)
i.e, \(\frac{1}{8}<\frac{1}{4}<\frac{1}{2}<\frac{6}{8}\)

Question 5.
Annan says the \(\frac{2}{6}\) th of the group of triangles given below are blue. Is he correct?

Solution:
No, he is not correct because of the total of 6 triangles 4 are blue, i.e \(\frac{4}{6}^{\text {th }}\) triangles are blue.

Question 6.
Joseph has a flower garden. Draw a picture which shows that \(\frac{2}{10}\) th of the flowers are red and the rest of them are yellow.
Solution:

Question 7.
Malarkodi has 10 oranges. If she ate 4 oranges, what fraction of oranges she was not eaten by her?
Solution:
\(\frac{\text { Oranges not eaten }}{\text { Total oranges }}=\frac{10-4}{10}=\frac{6}{10}\)

Question 8.
After sowing seeds on day one, Muthu observes the growth of two plants and records it. In 10 days, if the first plant grew \(\frac{1}{4}\) th of an inch and the second plant grew \(\frac{3}{8}\) th of an inch, then which plant grew more?
Solution:
Comparing \(\frac{1}{4}\) th of an inch and \(\frac{3}{8}\) th of an inch.
\(\frac{1}{4}=\frac{2}{8}<\frac{3}{8}\)
Second plant grew more.

Try These (Textbook Page No. 57 to 60)

Question 1.
Write the ratio of red tiles to blue tiles and yellow tiles to red tiles.

Solution:
(i) Red tiles to blue tiles = 2 : 3
(ii) Yellow tiles to red tiles = 2 : 2

Question 2.
Write the ratio of blue tiles to that of red tiles and red tiles to that of total tiles.

Solution:
The ratio of blue tiles to red tiles = 3 : 5
The ratio of red tiles to total tiles = 5 : 8

Question 3.
Write the ratio of shaded portion to the unshaded portions in the following shapes.

Solution:
(i) Ratio = 1 : 2
(ii) Ratio = 5 : 4

Question 4.
If the given quantity is in the same unit, put ‘✓’ otherwise put ‘ ✗’ in the table below.

Solution:

Question 5.
Write the ratios in the simplest form and fill in the table.

Solution:

Try These (Textbook Page No. 64)

Question 1.
For the given ratios, find two equivalent ratios and complete the table.

Solution:

Question 2.
Write three equivalent ratios and fill in the boxes.

Solution:

Question 3.
Find the given ratios, find their simplest form and complete the table.

Solution:

Try These (Textbook Page No. 70)

Question 1.
Fill the box by using cross product rule of two ratios
Solution:

By cross product rule we have 1 × □ = 5 × 8
1 × 40 = 40
∴ \(\frac{1}{8}=\frac{5}{40}\)

Question 2.
Use the digits 1 to 9 only once and write as many ratios that are in proportion as possible (For example \(\frac{2}{4}=\frac{3}{6}\))
Solution:

Students can Download Maths Chapter 4 Geometry Ex 4.2 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 1 Chapter 4 Geometry Ex 4.2

Miscellaneous Practice Problems

Question 1.
In the given figure, find PT given that l₁ || l₂

Solution:
Given that l₁ || l₂
∴ In ∆PQS and ∆PRT
∠P is common
∠Q = ∠R [∵ PR is the transversal for l₁ and l₂ corresponding angles]
∠S = ∠T [∵ corresponding angles]
∴ ∆PQS ~ ∆PRT [∵ By AAA congruency]
In similar triangles, corresponding angles are proportional.

Question 2.
From the diagram, prove that ∆SUN ~ ∆RAY

Proof:
From the ∆SUN and ∆RAY
SU = 10;
UN = 12;
SN = 14;
RA = 5,
AY = 6;
RY = 7
We have

Question 3.
The height of a tower is measured by a mirror on the ground by which the top of the tower’s reflection is seen. Find the height of the tower.
Solution:
The image and its reflection make similar shapes

Question 4.
In the figure, given that ∠1 = ∠2 and ∠3 ≡ ∠4 Prove that ∆MUG ≡ ∆ TUB.

Proof:

Question 5.
If ∆WAR ≡ ∆MOB, name the additional pair of corresponding parts. Name the criterion used by you.
Solution:

Given ∆WAR ≡ ∆MOB
∠RWA ≡ ∠BMO [∵ sum of three angles of a triangle are 180°]
∴ Criteria used here is angle sum property of triangles.

Question 6.
In the figure, ∠TMA ≡ ∠IAM and ∠TAM ≡ ∠IMA. P is the midpoint of MI and N is the midpoint of AI. Prove that ∆ PIN ~ ∆ ATM.

Solution:

Question 7.
In the figure, if ∠FEG = ∠1 then, prove that DG² = DE.DF.

Proof:

Question 8.
In the figure, ∠TEN ≡ ∠TON = 90° and TO = TE. Prove that ∠ORN ≡ ∠ERN

Solution:

Question 9.
In the figure, PQ ≡ TS, Q is the midpoint of PR, S is the midpoint TR and ∠POU ≡ ∠TSU. Prove that QU ≡ SU.

Proof:

Question 10.
In the figure ∆TOP ≡ ∆ARM . Explain why?
Solution:
In ∆TOP and ∆ARM
OP = RM given
∠TOP = ∠ARM = 90°
given ∠OTP = ∠RAM
given ∠OPT = ∠RMA Remaining angle, by angle sum property.
∴ By ASA criteria we can say that ∆TOP ≡ ∆ARM

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 4 Geometry Intext Questions

Try These (Textbook Page No. 80, 81)

Question 1.
Name all the line segments.

Solution:
\(\overline{\mathrm{AB}}, \overline{\mathrm{AE}}, \overline{\mathrm{EB}}, \overline{\mathrm{CD}}, \overline{\mathrm{CE}} \text { and } \overline{\mathrm{ED}}\)

Question 2.
If AB = 5 cm, say which of the following measures are correct in fig 4.9.

Solution:
Fig 4.9(i) and fig 4.9(ii) measures are correct.

Try These (Textbook Page No. 85)

Question 1.

1. Name the rays in the given figure.
2. What is the common point of all these rays?
Solution:
1. \(\overrightarrow{\mathrm{TA}}, \overrightarrow{\mathrm{TB}}, \overrightarrow{\mathrm{TC}} \text { and } \overrightarrow{\mathrm{TD}}\) are the rays given
2. Point T is the common point of all these rays.

Try These (Textbook Page No. 90, 95)

Question 1.
Which direction will you face if you start facing West and take three right turns clockwise?
Solution:
Will be facing South.

Question 2.
Which direction will you face if you start facing North and take two right turns anticlockwise?
Solution:
Will be facing South.

Question 3.
Adjust the hands of the clock for following time, note the angle made between the hour hand and the minute hand and write the type of angle.


Solution: