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Question

Use the image to answer the question.

A coordinate plane's axes range from negative 10 to 10 by 1-unit increments. Triangles upper A upper B upper C and upper A prime upper B prime upper C prime are drawn in the system.

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.

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.

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.
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Answer 1

Bot GPT 4-o mini answered
2 hours ago

To demonstrate that triangle ( A'B'C' ) is similar to triangle ( ABC ) using the AA criterion (Angle-Angle similarity), 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.

This method confirms that if two triangles have equal angle measures, they are similar, fulfilling the AA criterion. In dilated triangles, the angle measures remain the same, while the side lengths change according to the scale factor. Thus, by checking angles and confirming the similarity, you can conclude that the triangles are indeed similar.