Geometry Inequality Proof: show one side greater than another 
Can someone refresh my memory how to prove this. I am going to be tutoring a high school student. I know $\angle 1 = \angle 2$ and $EG$ is congruent to itself but where do I go from there?

Basic approach. The parallel postulate tells you that $m\angle DEG > m\angle EGF = m\angle EGD$, and therefore $DG > DE$ (larger sides are opposite larger angles, given that $\angle EGD$ is acute—it is half of an angle within a triangle—and $\angle EGD$ and $\angle DEG$ add up to less than $180$ degrees).
