Question

question 6 (multiple choice worth 1 points) (03.09 lc) if a figure has been dilated by a scale factor of ( \frac{1}{3} ), 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:

1. Recall the properties of dilation: Dilation preserves angle measures (so angles remain congruent) but changes side lengths by the scale factor. The AA (Angle - Angle) similarity postulate requires two pairs of congruent angles.
2. Analyze each option:

• Option 1: Translation is a rigid transformation that preserves shape and size. Since dilation preserves angle measures, after dilation, a translation can be used to map one angle onto another. This helps in showing that the corresponding angles of the original and dilated figures are congruent, which is useful for AA similarity.
• Option 2: Dilation does preserve orientation, so the statement "dilations do not preserve orientation" is wrong. Also, rotation is not needed here for AA similarity based on angle preservation from dilation.
• Option 3: Dilation changes side lengths (it scales them by the scale factor $\frac{1}{3}$), so it does not preserve side lengths. So this option's reasoning is incorrect.
• Option 4: Dilation does preserve orientation, so the statement "dilations do not preserve orientation" is wrong. Also, reflection is not the correct transformation here for AA similarity based on angle preservation from dilation.

Answer:

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