Question

prove that two sides of a triangle are congruent then the angle opposite to them are congruent (theorem)​

Answer 1

If two angles of a triangle are congruent , then the sides opposite to these angles are congruent. Draw ¯SR , the bisector of the vertex angle ∠PRQ . Therefore, by AAS congruent, ΔPRS≅ΔQRS .

Answer 2

prove that two sides of a triangle are congruent then the angle opposite to them are congruent

D is the midpoint of BC

BD = CD

Join A and D

By Reflexive Property ,

AB = AC

AD = AD

By SSS

ΔABD ≅ ΔADC

Since corresponding parts of congruent triangles are congruent,

∠B ≅ ∠C

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 , then AC≅BC