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