Question

In ∆pqr ,pe perpendicular bisector of QPR , Prove that PQ=QR.

Answer 1

In ∆PEQ and ∆ PER
PE=PE( common)
ang.QPE=ang.RPE (as PE bisects ang.QPR)
ang.QEP=ang.REP (each 90°)
Therefore ∆PEQ≈∆PER by AAS rule
By CPCT PQ=PR
Hope this helps

Answer 2

Given 
PE is perpendicular bisector of QPR
PE=RE
To prove = PQ=QR 
proof - In triangle PEQ and triangle PER
(s)  PE = RE  - GIVEN 
(A) PEQ = PER =90     BOTH ARE 90
(S) PE = PE  COMMON
So, ΔPEQ ≈ ΔPER  by SAS rule
Also, PQ = QR BY CPCT