Question

column a

1. angle - angle similarity theorem

2 side - side - side similarity theorem

1. side - angle - side similarity theorem

column b
a. if two of the corresponding sides of two triangles are proportional and the included angles are congruent, then the triangles are similar
b. if all three corresponding sides of two triangles are proportional, then the triangles are similar.
c. if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Explanation:

1. The Angle - Angle Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This matches option c.
2. The Side - Side - Side Similarity Theorem says that if all three corresponding sides of two triangles are proportional, then the triangles are similar. This corresponds to option b.
3. The Side - Angle - Side Similarity Theorem indicates that if two of the corresponding sides of two triangles are proportional and the included angles are congruent, then the triangles are similar. This is option a.

Answer:

1. c
2. b
3. a