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

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GPT-4o mini · Answer

To determine that the dilated triangle $ A'B'C' $ is similar to triangle $ ABC $ using the AA (Angle-Angle) criterion, the best approach is: **Find the angle measures of the original triangle and the dilated triangle, then compare proportionality of the ratio to the scale factor.** The AA criterion states that if two triangles have two corresponding angles that are equal, then the triangles are similar. Since dilation involves enlarging or reducing a triangle while maintaining the angle measures, you can simply check that the angles of triangle $ A'B'C' $ correspond to the angles of triangle $ ABC $ and are equal. If both pairs of corresponding angles are equal, then by the AA criterion, triangle $ A'B'C' $ is similar to triangle $ ABC $. The scale factor comes into play for side lengths but is not necessary for the similarity proof itself.