Question

in triangle ABC ,P and Q are two point on BC, such that angal apq=angle aqp and BP=QC. prove that∆ABP = ∆ACQ

Answer 1

Given : In ∆ABC, ∠APQ = ∠AQP and BP = CQ

To prove : ∆ABP and ∆ACQ are congruent.

Proof : In ∆APQ,

∠APQ = ∠AQP

Since side opposite to equal angles are equal.

AQ = AP

Now, ∠APQ + ∠APB = 180°

∠AQP + ∠AQC = 180°

∠APQ + ∠APB = ∠AQP + ∠AQC

∠APB = ∠AQC

In ∆ABP and ∆ACQ,

AP = AQ

∠APB = ∠AQC

BP = CQ

Hence by SAS congruency both triangles are congruent.

Q.E.D

Thanks!!!

Answer 2

Answer

by using SAS rule of congruencey