Question

1. two shapes are similar if their corresponding angles are congruent and their corresponding sides are proportional. triangle abc is similar to triangle def. what conjecture can you make about the two triangles?

triangle abc is bigger than triangle def.
\\( \overline { a b } \cong \overline { d e } \\)
\\( \angle a \cong \angle d \\)
triangle abc is smaller than triangle def.

Explanation:

Similar triangles have congruent corresponding angles. Just because two triangles are similar, we cannot say for sure which one is bigger or smaller (as similarity is about shape, not size). Also, \( \overline{AB}\cong\overline{DE} \) would imply congruence (not just similarity) if that was the case for all corresponding sides. But for similar triangles \( \triangle ABC\sim\triangle DEF \), the corresponding angles \( \angle A\) and \( \angle D\) (since \(A\) corresponds to \(D\) in similar triangles) are congruent.

Answer:

C. \( \angle A\cong\angle D \)