Question

which similarity postulate proves the two triangles are similar? image of two triangles with vertical angles and marked parallel sides options: sss similarity theorem, sas similarity theorem, aa similarity postulate, the triangles cannot be proven similar

Explanation:

Step1: Analyze Vertical Angles

The two triangles share a pair of vertical angles, so those angles are congruent.

Step2: Analyze Corresponding Angles

The triangles have two pairs of parallel sides (indicated by the arrows), so the corresponding angles formed by the transversal are congruent. Thus, we have two pairs of congruent angles.

Step3: Apply AA Similarity

By the AA (Angle - Angle) Similarity Postulate, if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Since we have two pairs of congruent angles (from vertical angles and corresponding angles from parallel lines), the AA Similarity Postulate applies.

Answer:

AA Similarity Postulate