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 ? (1 point) Responses Reflect the triangle across the x-axis and check for symmetry among the triangles with respect to the x-axis. Reflect the triangle across the x -axis and check for symmetry among the triangles with respect to the x -axis. 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. 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. Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor. Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor. Center the original triangle inside the dilated triangle and see if the side lengths are congruent by using the scale factor.

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 ? (1 point) Responses Reflect the triangle across the x-axis and check for symmetry among the triangles with respect to the x-axis. Reflect the triangle across the x -axis and check for symmetry among the triangles with respect to the x -axis. 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. 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. Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor. Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor. Center the original triangle inside the dilated triangle and see if the side lengths are congruent by using the scale factor.

Answer 1

To determine that the dilated triangle \( A'B'C' \) is similar to triangle \( ABC \) using the AA criterion (Angle-Angle criterion), the best response from the options provided is:

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.

This method allows you to establish the similarity by showing that two angles in triangle \( ABC \) are congruent to two angles in triangle \( A'B'C' \), which is sufficient to prove that the two triangles are similar based on the AA criterion. This criterion states that if two angles in one triangle are equal to two angles in another triangle, the triangles are similar.

The other options involve reflections, finding side lengths, or comparing ratios which do not directly apply the AA criterion for proving similarity through angle comparison.