Question

If you are using this figure to prove the isosceles triangle theorem which of the following would be the best strategy

Answer 1

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

 

∠P≅∠Q∠P≅∠Q

Proof:

Let SS be the midpoint of PQ¯¯¯¯¯PQ¯ .

Join RR and SS .

Since SS is the midpoint of  PQ¯¯¯¯¯PQ¯ , PS¯¯¯¯¯≅QS¯¯¯¯¯PS¯≅QS¯ .

By Reflexive Property ,

RS¯¯¯¯¯≅RS¯¯¯¯¯RS¯≅RS¯

It is given that PR¯¯¯¯¯≅RQ¯¯¯¯¯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¯ .