Question

Corresponding angles of ΔABC and ΔDEF are congruent. Does this prove that the triangles are congruent? Justify.

A) yes; AAA guarantees that all corresponding parts of the two triangles are congruent.

B) yes; AAA guarantees similarity and congruency because the triangles must have equal sides to have equal angles.

C) no; AAA only guarantees similarity because the lengths of the sides of the two triangles are not necessarily equal.

D) yes; AAA guarantees congruency because if at least two angles of a triangle are congruent to each other, then the triangles are congruent. Eliminate

Answer 1

no; AAA only guarantees similarity because the lengths of the sides of the two triangles are not necessarily equal.

Think about two equilateral triangles. Each triangle has three 60° angles; but, the side lengths of one of the triangles is not necessarily equal to the side lengths of the other triangle. So, they are similar, but they are not congruent.

Answer 2

C) The triangles could have the same shape but not necessarily the same size.