If we can prove that △ ECB and △ EAD are congruent, we can prove that AD≈ CB.
See solution.
Practice makes perfect
From the exercise we know that m∠ ECB and m∠ EAD have equal measures. We also know that E is the midpoint of AC, which means AE and EC are congruent. Let's add this information to the diagram.
Examining the diagram, we notice a pair of vertical angles around E.
Also we can see that △ AED and △ CEB have two pairs of congruent angles. Since the included side to these angles is also congruent, we know by the ASA (Angle-Side-Angle) Congruence Theorem that the triangles are congruent. Notice that AD and CB are corresponding sides. This means they are congruent.
