Question

AB is a line segment . p and q are points on opposite sides of AB such that each of them is equidistant from the points A and B show that the PQ is the perpendicular bisector of AB.​

Answer 1

Solution: In∠APQand∠BPQ

PA=PB

QA=QB

PQ=PQ

∠APQ

=

∼

∠BPQ(SSS)

∠APQ=∠BPQ

∠AQP=∠BQP

∠PAQ=∠PBQ

In ∠APCand∠BPC

∠APC=∠BPL

∠PAC=∠PBC

AP=BP

∠APC

=

∼

∠BPC (ASA)

∠PCA=∠PCB

AC=BC(C is Mid point of AB)

∠PCA+∠PCB=180

0

2∠PCA=180

0

∠PCA=90

0