Question

1. choose the true statements about the triangles. select all that apply. the measures of ∠s and ∠m are equal. the measures of ∠n and ∠q are equal. angles p and q are corresponding. angles n and q are corresponding. angles s and m are corresponding. angles n and r are corresponding. the measures of ∠n and ∠r are equal. these two triangles are similar by the angle - angle similarity theorem. these two triangles are not similar.

Explanation:

Step1: Recall corresponding - angle and similarity concepts

Corresponding angles in similar triangles are equal. For two triangles to be similar by AA - similarity, two pairs of corresponding angles must be equal.

Step2: Analyze each statement

Without seeing the triangles, assume we are working with the properties of similar triangles. Corresponding angles are in the same relative position in two similar triangles. If two triangles are similar by AA - similarity, then pairs of corresponding angles are equal.

Answer:

We need more information about the triangles (such as a figure showing the correspondence of vertices) to definitively select the true statements. But in general, if two triangles are similar by AA - similarity:

• Pairs of corresponding angles are equal. For example, if \(\triangle ABC\sim\triangle DEF\), \(\angle A=\angle D\), \(\angle B = \angle E\), \(\angle C=\angle F\) and the corresponding - angle statements would be true.
• If we know the triangles are similar by AA - similarity, the statement "These two triangles are similar by the Angle - Angle Similarity Theorem" would be true. If they are not similar, the statement "These two triangles are not similar" would be true. Without a figure or more context, we cannot select any of the given statements with certainty.