Question

isosceles triangle theorem​

Answer 1

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

∠P≅∠Q

Proof:

Let S be the midpoint of PQ¯¯¯¯¯ .

Join R and S .

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

By Reflexive Property ,

RS¯¯¯¯¯≅RS¯¯¯¯¯

It is given that PR¯¯¯¯¯≅RQ¯¯¯¯¯

Therefore, by SSS ,

ΔPRS≅ΔQRS

Since corresponding parts of congruent triangles are congruent,

∠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 , then AC¯¯¯¯¯≅BC¯¯¯¯¯ .

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