If two triangles have corresponding angles congruent, what is the implied relationship between the triangles?

If two triangles have corresponding angles congruent, what is the implied relationship between the triangles?

• A. They are similar
• B. They are congruent
• C. They are inversely similar
• D. They are neither similar nor congruent

Answer: (A)

When corresponding angles are congruent, the two triangles have the same shape. This is the AA (angle–angle) similarity idea: two angles match, so the third does as well, and the triangles are similar. Similar triangles have corresponding sides in proportional lengths, meaning one triangle can be a scaled version of the other. They’re not necessarily the same size, so they aren’t guaranteed to be congruent unless the scale factor is 1. So the implied relationship is that the triangles are similar.

When corresponding angles are congruent, the two triangles have the same shape. This is the AA (angle–angle) similarity idea: two angles match, so the third does as well, and the triangles are similar. Similar triangles have corresponding sides in proportional lengths, meaning one triangle can be a scaled version of the other. They’re not necessarily the same size, so they aren’t guaranteed to be congruent unless the scale factor is 1. So the implied relationship is that the triangles are similar.