Q. 14

# Prove that the angles opposite to equal sides of a triangle are equal

We have a triangle PQR where PS is the bisector of P

Now in ∆PQS and ∆PSR, we have:

PQ = PR (Given)

PS = PS (Common)

QPS = PRS (As PS is the bisector of P)

By SAS congruence rule

∆PQS PSR

Q = R (By Congruent parts of congruent triangles)

Hence, it is proved that the angles opposite to equal sides of a triangle are equal

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