If a figure has been dilated by a scale factor of one third, which transformation could be used to prove the figures are similar using the aa similarity postulate? a translation because it can map one angle onto another since dilations preserve angle measures of triangles. a rotation because it can change the orientation of a figure since dilations do not preserve orientation. a dilation because it can map one side onto another since dilations preserve side length of triangles. a reflection because it can change the orientation of a figure since dilations do not preserve orientation.

Explanation:

The AA similarity postulate is the Angle-Angle similarity postulate, which is used for triangles. It states that two triangles that have two congruent angles are similar.

So, what you must do is to find a transformation that permits to prove that two angles of the original figure are congruent to two angles of the dilated figure.

Let's see what the choices mean:

1) A translation because it can map one angle onto another since dilations preserve angle measures of triangles.

This is the correct choice.

Dilations, indeed, do not change the angle measures of triangles. Dilations change the length of the sides of the triangles but keep the inclination of the sides which means that the angles are preserved. So, the second part of this statement is correct.

As per the first part, a translation, which only moves the entire figure, keeping side lengths and angles, will let  you to overlap the vertices that you choose and prove that the angles are congruent.

If the dilation was made with one of the vertices as origin, then that vertex will not move, so you already have one vertex of the image over one vertex of the preimage, meaning that it is shown that one pair of angles are congruent. With the translation you will prove that other pair of triangles are congruent, and so you have the two pair on angles that prove by the AA similarity postulate that the figures are similar.

2) A rotation because it can change the orientation of a figure since dilations do not preserve orientation.

This is false because dilations do preserve orientation.

3) A dilation because it can map one side onto another since dilations preserve side lengths of triangles.

This is false because do not preserve side lengths.

4) A reflection because it can change the orientation of a figure since dilations do not preserve orientation.

This is false since reflections change the orientation you will not be able to overlap the vertices.

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