Question

Which postulate or theorem proves that these two triangles are congruent?



Responses

ASA Congruence Postulate
A S A congruence postulate

SAS Congruence Postulate
S A S congruence postulate

HL Congruence Theorem
H L congruence theorem

AAS Congruence Theorem
A A S congruence theorem
Triangle A B E and triangle D C E share vertex E. Segment A E and segment D E both have one congruent mark. Angle A and angle D both have one congruent mark.

Answer 1

AAS Congruence Theorem.

Reason: ∠A ≅ ∠D (given), ∠AEB ≅ ∠DEC (vertical angles at E), and AE ≅ DE (given). So the triangles have two angles and a corresponding non‑included side congruent, hence congruent by AAS.