CBSE Class 10 Maths Sample Paper 2019 | Q19A

This 2019 CBSE class 10 Maths 3 mark question is from Triangles. The key concept tested in this question is congruence of triangles - establishing that two triangles are congruent.

Question 19: In figure ∠1 = ∠2 and ΔNSQ ≈ Δ MTR, then prove that ΔPTS ~ ΔPRQ.

Video Explanation

Explanatory Answer | CBSE Sample Paper 2019 Question 19 Choice 1

Given Data

1. ∠1 = ∠2
2. ΔNSQ ⩰ ΔMTR

Property: If two angles in a triangle are equal then sides opposite to the two angles will be equal in length.
Because ∠1 = ∠2, PT = PS .....(1)

From the question, ΔNSQ ⩰ ΔMTR
Property: In congruent triangles, corresponding angles are equal.
∴ ∠NQS = ∠MRT
If ∠NQS = ∠MRT, then ∠PQR = ∠PRQ
∴ PR = PQ .....(2)

From 1 and 2
\\frac{\text{PT}}{\text{PR}}) = \\frac{\text{PS}}{\text{PQ}})
∠TPS = ∠RPQ (common)
∴ By SAS ΔPTS ~ ΔPRQ