If $\overline{ED}||\overline{AC}$and $\overline{EB}||\overline{DC}$, name all pairs of angles that must be congruent.

Postulate 10 states when a separate line travels through two lines which are having a parallel relation between them at that time the angles which are corresponding angles represents the congruent angles.

Theorem 3-2 states when a separate line travels through two lines which are having a parallel relation between them at that time the angles which are positioned on alternate interior side represents the congruent angles.

The definition of corresponding angles states that angles are corresponding angles when they are positioned on the lines but these lines are having the corresponding position.

So according to the definition of corresponding angles, postulate 10 and the provided information $\angle 5\cong \angle 2$.

The definition of alternate interior angles states that angles are alternate interior angles when they are positioned on the transversal but these angles are having the opposite sides along with this these angles are representing the non adjacent interior angles.

So according to the definition of alternate interior angles, theorem 3-2 and the provided information $\angle 2\cong \angle 8$.

The definition of transitive property of congruence states that whenever two angles are congruent and if any one of them is congruent to another angle that is beside those two angles then the second angle from first two angles also congruent to the another angle.

The definition of transitive property for the obtained congruent angles states that $\angle 5\cong \angle 8$.