Question

1. identify the postulate or theorem that can be used to prove the triangles congruent.

a. aas
b. cpctc
c. sas
d. asa
14 if a transversal

Explanation:

Step1: Analyze the given information

We have two triangles formed by a diagonal in a figure with two pairs of parallel sides (indicated by the arrows). The two sides of the triangles are marked as equal (the two segments between the parallel sides). The included angle (the angle between the two sides) is common to both triangles.

Step2: Recall the congruence postulates

• AAS (Angle - Angle - Side): Requires two angles and a non - included side.
• CPCTC (Corresponding Parts of Congruent Triangles are Congruent): Is used after proving triangles congruent, not to prove them congruent.
• SAS (Side - Angle - Side): Requires two sides and the included angle. Here, we have two sides (marked equal) and the included angle (common angle) between them.
• ASA (Angle - Side - Angle): Requires two angles and the included side.

Answer:

C. SAS