Question

Courtney says that △ABC ≅ △EBD by the SAS congruence postulate. Do you agree or disagree? Explain.

Suppose it is also known that CAB ≅ DEB. Which postulate or theorem can be used to prove that ABC ≅ EBD? Justify your answer.
(a) SAS Congruence Postulate
(b) ASA Congruence Postulate
(c) SSS Congruence Postulate
(d) Corresponding Angles Postulate

Answer 1

Courtney's claim of △ABC ≅ △EBD via SAS is incorrect without side lengths. The correct postulate is ASA, given that two angles and the included side are congruent between the triangles.

Step-by-step explanation:

I disagree with Courtney's assertion that △ABC ≅ △EBD by the SAS Congruence Postulate, because she has not mentioned any side lengths to support that. Instead, considering it is known that ∠CAB ≅ ∠DEB, we can conclude that △ABC ≅ △EBD by the ASA Congruence Postulate. This conclusion is justified because we now have two angles and the included side that are congruent. The ASA Congruence 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.