Question

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?

A(-4,-6)
B(3,-6)
C(-2,-1)
A'(-4,-3)
B'(10,-3)
C'(0,7)

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 if the dilated triangle A'B'C' is similar to triangle ABC using the AA (Angle-Angle) criterion, we need to establish that the corresponding angles of the two triangles are equal.

Out of the provided options, the most relevant choice that aligns with the AA criterion involves examining the angle measures of both triangles. This would allow us to demonstrate that the triangles have corresponding angles that are equal, which suffices to prove similarity.

Thus, the best option here is:

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

This option explicitly mentions finding the angle measures, which directly relates to the AA criterion for similarity, as two triangles are similar if two angles of one triangle are congruent to two angles of another triangle. Once we establish that the angles are equal, we can conclude that the triangles are similar.