Question

Given:

AD | | BC
AD = BC

Prove:
ADM BCM

Which of the following reasons will complete the proof?

SAS
ASA
SSS

Answer 1

The correct answer is ASA.

If you look at the steps given in the proof, you will see that are are given two different angles that are congruent. You also have a side that is in between the two angles. Therefore, we have ASA.

Answer 2

Answer:- "ASA congruence postulate" is the reason which completes the proof.

Explanation:-

Given:- AD | | BC and AD = BC

To prove:- ΔADM ≅ΔBCM

Proof:- Statement Reason

1. AD=BC [Given]

2. ∠1=∠3 ; ∠2=∠4 [If lines parallel, then alternate interior angles are equal]

3. ΔADM ≅ΔBCM [ASA congruence postulate]

Thus, "ASA congruence postulate" is the reason which completes the proof.