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. 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. 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. Center the original triangle inside the dilated triangle and see if the side lengths are congruent by using the scale factor.

Question

GPT-4o mini · Answer

To determine that the dilated triangle $ A'B'C' $ is similar to triangle $ ABC $ using the AA (Angle-Angle) criterion, you would want to compare the angle measures of both triangles. Thus, the correct response from the options provided is: **Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor.** This response essentially aligns with the AA criterion, which states that if two triangles have two corresponding angles that are equal, then the triangles are similar. In the case of dilation, the angles of the original triangle and the dilated triangle remain unchanged, thereby fulfilling the similarity condition based on angles.