The two triangles in the diagram can be proven congruent using the SAS (Side-Angle-Side) congruence postulate. Here's the reasoning:

1. M is the midpoint of $\overline{AX}$: This implies $\overline{AM} \cong \overline{MX}$ (first pair of congruent sides).
2. Vertical angles: $\angle AMW \cong \angle BMX$ (these are congruent because vertical angles are always equal).
3. Given markings: $\overline{WM} \cong \overline{BM}$ (second pair of congruent sides).

Thus, triangles $\triangle WMA$ and $\triangle XMB$ are congruent by SAS.

Would you like additional clarifications or detailed steps?

Here are 5 related questions to expand your understanding:

1. How can you identify congruent angles in diagrams with intersecting lines?
2. What are the other congruence postulates aside from SAS?
3. Can these triangles be congruent by SSS instead? Why or why not?
4. How is the concept of a midpoint used in proving congruence?
5. What are examples where vertical angles are used in congruence proofs?

Tip: When working with intersecting triangles, always check for shared sides or vertical angles first!