Which triangles are similar by the angle-angle criterion for similarity of triangles?
A triangle is said to be similar to another triangle if the corresponding sides are in proportion to each other and the measures of corresponding angles are congruent.
Answer: By AAA if two corresponding angles are congruent then the triangle is similar.
Let's explain in detail.
So, ∆ ABC ~ ∆ XYZ, if ∠ A ≅ ∠ X and ∠ B ≅ ∠ Y
Therefore, by the angle sum property of the triangle, the measure of the third angle will be congruent.
⇒ ∠ C ≅ ∠ Z