Which criterion states that two triangles are similar if two angles of one are congruent to two angles of the other?

• A. CPCTC
• B. HL Congruence
• C. SSS for Similarity
• D. AA Similarity

Answer: (D)

The key idea is that a pair of triangles is similar when their corresponding angles match. If two angles in one triangle are congruent to two angles in the other, the third angles must also be congruent because the interior angles of any triangle add up to 180 degrees. With all three corresponding angles equal, the triangles are similar by the Angle-Angle Similarity criterion. Once they’re similar, the ratios of their corresponding sides are equal, which is the defining feature of similarity.

The other concepts aren’t the criterion here: CPCTC refers to corresponding parts of congruent triangles and is a consequence after establishing congruence, not a criterion for similarity; HL Congruence applies to right triangles and deals with congruence, not similarity; SSS for Similarity is a different route that uses proportional sides rather than angles.