Question

Triangle ABC has been translated to create triangle A'B'C'. Angles C and C' are both 32 degrees, angles B and B' are both 72 degrees, and sides BC and B'C' are both 5 units long. Which postulate or theorem below would prove the two triangles are congruent?

Answer 1

The ASA (Angle-Side-Angle) postulate

Explanation:

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Here, congruent angles are C and B with C' and B' and included side congruent is the side BC with the side B'C'

Hence,triangle ABC is congruent to triangle A'B'C' by the ASA postulate

Answer 2

we know that

The ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

In this problem

The two congruent angles are C and B with C' and B'

The included side congruent is the side BC with the side B'C'

therefore

triangle ABC is congruent with the triangle A'B'C' by the ASA postulate

the answer is

The ASA (Angle-Side-Angle) postulate