# What is one proof of the converse of the Isosceles Triangle Theorem?

##### 1 Answer

Nov 16, 2015

See explanation.

#### Explanation:

The converse of the Isosceles Triangle Theorem states that *if two angles #hat A# and #hat B# of a triangle #ABC# are congruent, then the two sides #BC# and #AC# opposite to these angles are congruent*.

The proof is very quick: if we trace the bisector of

We can prove that the triangles

#hat A cong hat B# (hypotesis of the theorem)#hat(ACP) cong hat(BCP)# since#CP# lies on the bisector of#hat C# #CP# is a shared side between the two triangles

Since the triangles