Which triangles are similar by the angle-angle criterion for similarity of triangles?

Solution:

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.

The similarity between two triangles can be represented using the symbol '~' and the angles can be represented congruent by using the symbol '≅'.

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

Thus, the triangles that have congruent angles are similar with the AAA similarity criterion.

Which triangles are similar by the angle-angle criterion for similarity of triangles?

Summary:

By AAA if two corresponding angles are congruent then the triangle is similar.