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

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.
Samacheer Kalvi 8th Maths Term 1 Chapter 4 Geometry Additional Questions 1
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.
Samacheer Kalvi 8th Maths Term 1 Chapter 4 Geometry Additional Questions 40
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

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

Short Answers [3 Marks]

Question 1.
In the figure with respect to ABEP and CPD prove that BP × PD = EP × PC.
Samacheer Kalvi 8th Maths Term 1 Chapter 4 Geometry Additional Questions 51
Solution:
Proof:
In ∆EPB and ∆DPC
∠PEB = ∠PDC = 90° [given]
∠EPB = ∠DPC [Vertically opposite angles]
∠EPB = ∠PCD [∵ Remaining angles]
Thus,
Samacheer Kalvi 8th Maths Term 1 Chapter 4 Geometry Additional Questions 50

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:
Samacheer Kalvi 8th Maths Term 1 Chapter 4 Geometry Additional Questions 52
AB = AP + PB
= 3 + 6 cm = 9 cm
AC = AQ + QC = 510 cm = 15
Samacheer Kalvi 8th Maths Term 1 Chapter 4 Geometry Additional Questions 53
Samacheer Kalvi 8th Maths Term 1 Chapter 4 Geometry Additional Questions 54

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