Question

In a triangle ABC, AB = AC. Suppose P is point on AB and Q is a point on AC such that AP = AQ. Prove that ΔAPC ≅ ΔAQB.

Answer 1

Given: AB = AC and AP = AQ

To Prove: ΔAPC ≅ ΔAQB

Proof:

In ΔAPC and ΔAQB:

AC = AB (Given)

∠A = ∠A (Common)

AP = AQ (Given)

⇒ ΔAPC ≅ ΔAQB (SAS congruency)