How can a similarity transformation be used to determine that the AA criterion proves the dilated triangle A'B'C' is similar to triangle ABC?

Question

A. Reflect the triangle across the x-axis and check for symmetry among the triangles with respect to the x-axis
B. Center the original triangle and the dilated triangle and see if the side lengths are congruent by using the scale factor
C. Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor
D. Translate the dilated triangle so one of its angles exactly matches the corresponding angle in the original triangle; repeat using a different pair of angles

Answer 1

To determine that triangle A'B'C' is similar to triangle ABC using the AA criterion with respect to similarity transformations, the most appropriate option is:

C. Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor.

The AA (Angle-Angle) criterion states that two triangles are similar if two corresponding angles are congruent. In the case of a dilated triangle, the angles remain the same while the side lengths change by the scale factor. By confirming that the angles in triangle A'B'C' are equal to those in triangle ABC, you can conclude that they are similar triangles, satisfying the AA criterion for similarity.

Options A, B, and D do not directly reference the AA criterion or provide a clear method of verifying similarity through angle measures, making option C the best choice in this context.