Question

determine if the triangles to the right are similar, and explain how you know. a. the triangles are not similar because none of the corresponding pairs of angles are equal. b. the triangles are similar because all of the ratios of corresponding side lengths are equal. c. the triangles are not similar because not all of the ratios of corresponding side lengths are equal and not all of the corresponding pairs of angles are equal. d. the triangles are similar because all of the corresponding pairs of angles are equal.

Explanation:

Step1: Recall similarity criteria

Two triangles are similar if their corresponding angles are equal (AA - Angle - Angle similarity), or if the ratios of their corresponding side - lengths are equal (SSS - Side - Side - Side similarity, or SAS - Side - Angle - Side similarity).

Step2: Analyze options

Option A is correct because if none of the corresponding pairs of angles are equal, the triangles cannot be similar. Similarity is based on either equal angles or proportional sides. If angles are not equal, the triangles are not similar.

Answer:

A. The triangles are not similar because none of the corresponding pairs of angles are equal.