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SAS

Corresponding Parts of Congruent Triangles are
Congruent (CPCTC)

Converse of the Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the
triangle is isosceles and the sides opposite those angles are congruent

Converse of the Isosceles Triangle Theorem

We’ll prove this one together, as well. We’ll use above and assume that .

Statement Justification

Given

Reflexive Property of Congruence

Given

ASA

Corresponding Parts of Congruent Triangles are
Congruent (CPCTC)

is isosceles Definition of Isosceles

Basically, we proved that the triangle is congruent to itself. However, this example shows that the order
that the vertices of the congruent triangles are named is important. That order tells us about the
congruence of corresponding parts of the congruent triangles.

Question

Which pair of statements can be used to prove that ?