10+

Question

9
8
C'
7
6
5
4
3
2
C
1
-0-
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-2
-3
B
-4
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-6
A
B
-7
-8
-9
-10-
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.

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.

Answer 1

To determine that the triangle \( A'B'C' \) is similar to triangle \( ABC \) using the AA (Angle-Angle) criterion through a similarity transformation, you would:

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

This method relies on the property that when triangles are similar, corresponding angles are equal. In the case of a dilation, the angle measures of the triangle remain unchanged, and since all corresponding angles are equal, the AA criterion confirms that the triangles are similar.