Question

Determine which postulate or theorem can be used to prove that

ABDE ACBD. A B
A. ASA
B. AAS
C. SSS
D. SAS

Answer 1

The correct choice to prove that ABDE ACBD is D. SAS (Side-Angle-Side).

Step-by-step explanation:

SAS is a postulate that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. In this case, we can use SAS to prove that ABDE ACBD.

We can see that triangle ABD and triangle ABC share the following:
Side AB is congruent to side AB

Side BD is congruent to side CB

Angle A is congruent to angle C

Therefore, we have two sides and the included angle of one triangle congruent to two sides and the included angle of another triangle, satisfying the conditions for SAS. Therefore, the correct choice to prove that ABDE ACBD is D. SAS (Side-Angle-Side).