Question

In the given figure, AP=AQ , BP=BQ . Prove that AB is the bisector of angle PAQ and angle PBQ .​

Answer 1

Answer:

In triangle APB and AQB

Ap=AQ

BP=BQ

AB is common side

Triangle APB congruence AQB(s-s-s congruence rule)

Angle PAB= angle QAB

Angle PBA= angle ABQ

Therefore AB is the bisector of angle PAQ and angle PBQ(Proved)

Answer 2

Step-by-step explanation:

In∆APB &∆ABQ

AP=AQ -------(given)

BP=BQ -------(given)

AB=AB -------(common)

∆APB≈∆ABQ -------(SSS)

angle PAB=angle BAQ------(CPCT)

AB is bisector of angle PAQ

anglePBA=angle ABQ------(CPCT)

AB is bisector of angle PBQ

Hence proved