Question

Given: AM=MB,DM=MC. Which of the following triangle congruency theorems proves ΔAMD≅ΔBMC?

a. ASA
b. SAS
c. SSS
d. SSA

Answer 1

The triangles ΔAMD and ΔBMC can be proven congruent using the SAS (Side-Angle-Side) congruency theorem.

Step-by-step explanation:

The triangles ΔAMD and ΔBMC can be proven congruent using the

SAS (Side-Angle-Side)

congruency theorem.

Given that AM=MB, DM=MC, we have two pairs of congruent sides. We can also conclude that ∠ AMD = ∠BMC since they are corresponding angles. Additionally, we have the shared side AD.

Therefore, by the SAS congruency theorem, we can conclude that ΔAMD ≅ ΔBMC.