Question

Complete the given proof with the appropriate statement:

Given:
AM = BM
DM = CM
∠AMD = ∠BMC

Prove: △AMD ≅ △BMC

Answer 1

To prove that △AMD is congruent to △BMC, we can use the side-angle-side (SAS) congruence postulate. By showing that △ADM is congruent to △CBM using the angle-side-angle (ASA) congruence postulate, and then using the common side segment AM = BM, we can conclude that △AMD ≅ △BMC.

Step-by-step explanation:

To complete the given proof and prove that △AMD is congruent to △BMC, we can use the side-angle-side (SAS) congruence postulate.

Given that AM = BM, DM = CM, and ∠AMD = ∠BMC.

First, we can show that △ADM is congruent to △CBM by the angle-side-angle (ASA) congruence postulate. We know that ∠AMD = ∠BMC and DM = CM. Then, by using the common side segment AM = BM, we can conclude that △AMD ≅ △BMC by the SAS congruence postulate.