Question

What theorem should be used before we prove the triangles are congruent?

Answer 1

We are asked to prove the congruency of the triangles GFM and BCM. To prove congruency we initially prove that angles:

`\begin{gathered} \measuredangle BMC \\ \measuredangle GMF \end{gathered}`

Are congruent by the vertical angles theorem.

Also, since segments CB and FG are parallel, this means that:

`\measuredangle MFG\cong\measuredangle MCB`

This is by alternate interior angles theorem.

Finally, the congruency is proven by ASA (Angle Side Angle) since we have two congruent pairs of angles and we are given that sides CM and MF are congruent. Therefore, the triangles are congruent.