You have to show that corresponding sides and corresponding angles are congruent.
See solution.
Practice makes perfect
Let's first highlight the two triangles we are working with.
To prove that these triangles are congruent, △ AEB ≅ △ CED, we have to show that corresponding sides are congruent and that corresponding angles are congruent.
Sides
From the given information, we can say that at least two sides are congruent, namely the ones marked as such: AB and DC. Additionally, we know that E is the midpoint of AC as well as the midpoint of DB. The definition of a midpoint is that it cuts a segment in half. We can therefore say that
AE≅EC and BE≅ED.
Let's show this in our diagram.
Thus we have three pairs of congruent sides.
Angles
Finally, we have to show that corresponding angles are congruent. First, we notice that ∠ AEB and ∠ CED are vertical angles. According to the Vertical Angles Congruence Theorem, they are congruent.
Let's proceed with the remaining two sets of angles. Since AB∥ DC we can, by viewing BD and AC as transversals, show that ∠ ABD and ∠ CDB as well as ∠ BAC and ∠ DCA are alternate interior angles and therefore congruent.
Since corresponding sides and corresponding angles are congruent, we have proven that △ AEB ≅ △ CED.
