Question

Give me
Isoceles triangle theorem with proof

Answer 1

Answer:

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

∠P≅∠Q

Step-by-step explanation:

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⎯⎯⎯⎯⎯ .

PQ=base of the triangle .

∠P≅∠Q

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

                                                                           hence proved.

Answer 2

Answer :-

________________________

Isosceles Triangle Theorem

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¯ .