Question

In the given figure AP = AQ, BP = BQ. Prove that AB is the bisector
of ZPAQ and ZPBQ​

Answer 1

Answer: its all about proving if its a bisector

Step-by-step explanation:

trianglle PAQ and  triangle PBQ

AP=AQ (given)

BP=BQ (given)

AB=BA (common)

so triangle PAQ congruent to triangle PBQ

so AB is the bisector of quadrilateral APBQ

Answer 2

Answer:

In △APB and △AQB

AP=AQ (Given)

BP=BQ (Given)

AB=AB (Common Side)

∴△APB≅△AQB (S.S.S. congruency)

⇒∠PAB=∠QAB (CPCT)

⇒∠PBA=∠QBA (CPCT)

Thus, AB is the bisector of ∠PAQ and ∠PBQ.