Question

Which of the following choices must be true in order for ΔABC ≅ ΔEDC by the AAS congruency theorem? ∠B ≅ ∠D ∠A ≅ ∠E AC ≅ EC AB ≅ DE

Answer 1

∠A ≅ ∠E

Explanation:

The AAS (Angle-Angle -Side) congruence theorem implies that triangles ABC and EDC are congruent if both have equal two angles and a non included side.

In the given figures,

<ACB ≅ <ECD (vertical opposite angles)

BC ≅ DC (congruence property)

<ABC ≅ <EDC (alternate angles property)

∠A ≅ ∠E (alternate angle property)

With respect to AAS congruence theorem, ∠A ≅ ∠E is the correct option.