.
If a figure has been dilated by scale factor of 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 figure since dilations do not preserve orientation: A dilation because it can map one side onto another since dilations preserve side length of triangles. reflection because it can change the orientation of a figure since dilations do not preserve orientation.
The Correct Answer and Explanation is:
The correct answer is a dilation.
Explanation:
When we are dealing with the similarity of two figures, the AA (Angle-Angle) similarity postulate comes into play when we can show that two angles of one figure are congruent to two angles of another figure. The AA postulate states that if two triangles have two pairs of corresponding angles that are congruent, then the triangles are similar.
In the context of dilations, a dilation is a transformation that enlarges or reduces a figure by a specific scale factor, but it preserves the shape of the figure. This means that the corresponding angles of the dilated figure remain congruent to the angles of the original figure. Since dilations do not change the angles, they automatically preserve the angle measures of the figure, making the figures similar if corresponding angles are congruent.
Why Other Transformations Are Not Suitable:
- Translation: A translation moves the figure along a straight path without rotating or resizing it. While translations preserve the shape and size of the figure, they do not directly prove similarity because they do not change the scale or proportions of the figure. Moreover, translation does not change the angles or prove similarity by the AA postulate.
- Rotation: A rotation turns the figure around a fixed point. While it preserves angle measures, it can change the orientation of the figure, making it unsuitable for proving similarity using the AA postulate since orientation does not affect similarity. The AA postulate only concerns congruent angles and does not require specific orientation.
- Reflection: A reflection flips the figure over a line, changing its orientation. Like rotation, this can alter the orientation of the figure, which is not relevant for the AA similarity postulate. Since reflections do not preserve the orientation and can create an image that appears flipped, they cannot be used to prove similarity by AA.
Conclusion:
Dilation is the correct transformation for proving that figures are similar because it preserves angles and proportionality, both key components in similarity.
