Definition of Similar Figures Quick Check 2 of 52 of 5 Items Question Use the image to answer the 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 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. 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. Skip to navigation page 16 of 16 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Question

Definition of Similar Figures Quick Check 2 of 52 of 5 Items Question Use the image to answer the 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 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. 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. Skip to navigation page 16 of 16 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

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1 answer
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Answer 1

Bot GPT 4-o mini answered
13 days ago

To determine that the dilated triangle \( A'B'C' \) is similar to triangle \( ABC \) using a similarity transformation and the AA criterion (Angle-Angle criterion), the correct response would likely be:

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

This approach involves verifying that the angles of both triangles are congruent, which is a requirement for similarity according to the AA criterion. If two triangles have two corresponding angles that are equal, then the triangles are similar, regardless of their size. The use of scale factors would then confirm the proportionality of their sides.