Question

prove that if two sides of a triangle are congruent then the opposite of them are congruent​

Answer 1

we will take ∆PRQ

Since S is the midpoint of PQ

PS=QS

Join R and S

By Reflexive Property ,

RS=RS

PR= RQ

Therefore, by SSS ,

ΔPRS≅ΔQRSΔPRS≅ΔQRS

Since corresponding parts of congruent triangles are congruent,

∠P≅∠Q∠P≅∠Q

The converse of the Isosceles Triangle Theorem is also true.

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

If ∠A≅∠B∠A≅∠B , then AC≅BC

AC≅BC