Question

in fig .9.43, p and q are two points on equal side ab and ac of an isosceles triangle abc such that ap=aq . prove that bq=cp

Answer 1

Consider triangle abq and acp
ab = ac (given that abc is an isosceles triangle
angle a = angle a ( common
aq = ap (given in question
therefore by SAS criteria
triangle abq is congruent to triangle acp
therefore by CPCT bq = cp
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Answer 2

Consider triangle abq and acp

ab = ac (given that abc is an isosceles triangle

angle a = angle a ( common

aq = ap (given in question

therefore by SAS criteria

triangle abq is congruent to triangle acp

therefore by CPCT bq = cp