Exercise 18 Page 269

Let's begin by analyzing the desired outcome of our proof. We want to show that $△ADC$ is congruent to $△EDG.$ The triangles share the angles $\angle A$ and $\angle E$ with $△BAD$ and $△FED,$ respectively. Let's show that these triangles are congruent first.

We are given that $\overline{AD}\cong \overline{ED}.$ This is how we will begin our proof! We are also given that $D$ is the midpoint of $\overline{BF}.$ Thus, by the definition of a midpoint, it divides $\overline{BF}$ into two congruent segments $\overline{FD}$ and $\overline{BD}.$