Question

Given: (AB)= (DE) and angle A = angle D which of the following methods could be used to prove ∆ABC = ∆DEC?

A. Side-Angle-Side (SAS) congruence theorem.
B. Angle-Angle-Side (AAS) congruence theorem.
C. Side-Side-Side (SSS) congruence theorem.
D. Angle-Side-Angle (ASA) congruence theorem.

Answer 1

The correct method to prove ∆ABC = ∆DEC is the Angle-Side-Angle (ASA) congruence theorem, which 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.

Step-by-step explanation:

The correct method to prove ∆ABC = ∆DEC given that (AB) = (DE) and angle A = angle D is the Angle-Side-Angle (ASA) congruence theorem. This theorem 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.

In this case, angle A is congruent to angle D, and segment AB is congruent to segment DE. Therefore, using the ASA congruence theorem, we can conclude that ∆ABC is congruent to ∆DEC.