Question

if we know they are congruent, and they are on either side of a transversal (eo), what kind of relationship do the two angles have?
supplementary angles
vertical angles
alternate interior angles
edit my response
correct!
why does this help us prove that the opposite sides of the efgh are parallel?

Explanation:

When two angles are congruent and on either side of a transversal, they are alternate interior angles. By the Alternate Interior Angles Theorem, if alternate interior angles are congruent, then the lines (in this case, the opposite sides of the EFGH) are parallel.

Answer:

Alternate interior angles are congruent. By the Alternate Interior Angles Theorem, if alternate interior angles are congruent, then the lines (opposite sides of EFGH) are parallel.