Question

In the adjoining figure, P and Q are two points on equal sides AB and AC of an isosceles triangle ABC such that AP = AQ. Prove that BQ = CP.

Answer 1

let

in triangle abc

pq is parallel to bc(isoscales triangle apq is formed and ap=aq)

so join points pc and bq

then in trianglebqc and pbc

angle pbc=angle bcq (equal angles of isoscales triangle)

....1

bc is the common side....2

angle bpc=angle bqc(opposite to alternate angles).....3

from sas test

triangle pbc= triangle qcb

by csst

bq=qc

and pc= bq

thus proved