Final answer:
Without information about the sides, the AA (Angle-Angle) theorem is likely the correct triangle similarity theorem to use, as it requires two pairs of congruent angles between triangles, and we know at least one angle in the triangles is congruent.
Step-by-step explanation:
To determine which triangle similarity theorem proves that two triangles are similar when given that angles ZABE and EDC both equal 100°, we need to consider the available theorems. The primary theorems for triangle similarity are AA (Angle-Angle), SSS (Side-Side-Side), and SAS (Side-Angle-Side). The AA theorem states that two triangles are similar if two angles of one triangle are congruent to two angles of the other triangle. Since we know two angles are equal, we can use the AA theorem to establish triangle similarity, provided we have or can deduce one more pair of congruent angles between the triangles.
We would need to know corresponding sides are in proportion for the SSS theorem or one pair of proportional sides adjacent to a congruent angle for the SAS theorem. Since the question does not provide information about the sides, the AA theorem is most likely the appropriate similarity theorem to apply in this scenario. As the information is incomplete, we're assuming the existence of an additional pair of congruent angles. Thus, with the given information, AA theorem would be the theorem we use to prove that two triangles are similar.