From the diagram we know that \overline{ER}\cong \overline{BA} and \overline{RM}\cong \overline{AC}. If we want these triangles to be congruent by SAS we will need to identify the corresponding angles that complete the congruency theorem.

\angle{R}\cong \angle{A}

Be sure that the angle identified is in between the given congruent sides.

The best way to show that two triangles are congruent is to label any given information or information that can be inferred on the diagram. In this example, we can label \overline{DE} \cong \overline{EF} because E is a midpoint. Take a look at the labeled diagram:

We can then deduce by which theorem the triangles are congruent.

From the diagram we know that \overline{HD} \cong \overline{FG} and \overline{EH} \cong \overline{GE}. Since E is the midpoint of \overline{DF}, we know that \overline{DE} \cong \overline{EF}. So, we can conclude that \triangle{DEH}\cong \triangle{FEG} by Side-Side-Side congruence (SSS).

It's important to remember to justify the statements we make when showing two triangles are congruent, such as using the definition of a midpoint to show why \overline{DE} \cong \overline{EF}, in order for our explanation to be valid.