Question 17 - CBSE Sample Paper Class 10 - 2017-18

Last updated at Dec. 21, 2017 by Teachoo

In given figure ∠1 = ∠2 and ∆NSQ ≅ ∆MTR , then prove that ∆PTS ~ ∆ PRQ .

OR

In an equilateral triangle ABC, D is a point on the side BC such that BD = 1/3 BC. Prove that 9AD ² = 7AB ²

Download Sample Paper of Class 10 here https://www.teachoo.com/cbse/sample-papers/

Question 17

In an equilateral triangle ABC, D is a point on the side BC such that BD = 1/3 BC. Prove that 9AD ² = 7AB ²

This is exactly same as Ex 6.5, 15.

Check answer here

Transcript

Question 17 In given figure ∠1 = ∠2 and ∆NSQ ≅ ∆MTR , then prove that ∆PTS ~ ∆ PRQ . Given: ∠ 1 = ∠ 2 & ΔNSQ ≅ ΔMTR To Prove: ΔPTS ∼ PRQ Proof: Given ΔNSQ ≅ ΔMTR ∴ ∠ NQS = ∠ MRT i.e. ∠ PQR = ∠ PRQ In Δ PST By angle sum property ∠ P + ∠ 1 + ∠ 2 = 180° Since ∠ 1 = ∠ 2 given ∠ P + ∠ 1 + ∠ 1 = 180° ∠ P + 2 ∠ 1 = 180° In Δ PQR By angle sum property ∠ P + ∠ PQR + ∠ PRQ = 180° From (1), ∠ PQR = ∠ PRQ ∠ P + ∠ PQR + ∠ PQR = 180° ∠ P + 2 ∠ PQR = 180° Now, Right side of (2) and (3) are same So, from (2) and (3) ∠ P + 2 ∠ 1 = ∠ P + 2 ∠ PQR 2 ∠ 1 = 2 ∠ PQR ∠ 1 = ∠ PQR In ΔPTS & Δ PRQ ∠P = ∠P ∠ PST = ∠ PQR ∴ ΔPTS ∼ PRQ Hence proved

CBSE Sample Paper Class 10 - 2017-18

Question 17 You are here

Serial order wise →

Class 10

Sample Papers, Previous Year Papers and Other Questions

CBSE Sample Paper Class 10 - 2017-18

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.

Question 17 - CBSE Sample Paper Class 10 - 2017-18

In given figure ∠1 = ∠2 and ∆NSQ ≅ ∆MTR , then prove that ∆PTS ~ ∆ PRQ .

OR

In an equilateral triangle ABC, D is a point on the side BC such that BD = 1/3 BC. Prove that 9AD 2 = 7AB 2

Question 17

In an equilateral triangle ABC, D is a point on the side BC such that BD = 1/3 BC. Prove that 9AD 2 = 7AB 2

In an equilateral triangle ABC, D is a point on the side BC such that BD = 1/3 BC. Prove that 9AD ² = 7AB ²

In an equilateral triangle ABC, D is a point on the side BC such that BD = 1/3 BC. Prove that 9AD ² = 7AB ²