Final answer:
Triangle AED is similar to triangle BEC because line AD is parallel to line BC, making their alternate interior angles congruent, which satisfies the Angle-Angle (AA) criterion for similarity of triangles.
Step-by-step explanation:
To determine that triangle AED is similar to triangle BEC, given that line AD is parallel to line BC, we can use the Angle-Angle (AA) criterion for similarity between triangles. When two lines are parallel, any angles that intersect those lines are either congruent or supplementary.
If we have a transversal that intersects AD and BC, then the alternate interior angles would be congruent. Specifically, angle AED would be congruent to angle BEC, and angle DEA would be congruent to angle CEB, by the Alternate Interior Angles Theorem, since AD is parallel to BC. With two pairs of congruent angles, we can conclude that triangles AED and BEC are similar by AA criterion.
This relationship can be seen in the fact that similar triangles have corresponding angles that are equal and sides that are proportional. Thus, we can say triangle AED is similar to triangle BEC because they have at least two congruent angles