If a figure has been dilated by a scale factor of 1/3 which transformation could be used to prove the figures are similar using the AA similarity postulate?

Question

Mathematics

Brent Manning

10 February, 01:39

If a figure has been dilated by a scale factor of 1/3 which transformation could be used to prove the figures are similar using the AA similarity postulate?

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Answers (2)

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Ball · Answer 1

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

Step-by-step explanation:

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Kaya Warner · Answer 2

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

Step-by-step explanation:

In order to prove the two triangles by AA postulate, we must meet the conditions of the AA similarity postulate that says-

"Two triangles that have two congruent angles are similar".

So, we have to prove at least two corresponding angles of the given two triangles congruent.

One triangle is the dilation of the other. When we dilate a figure, the things that change are:

1. Lengths - Dilation changes the lengths of each side of the figure.

2. Size - Dilation changes the size of the figure.

When we dilate a figure, the things that do not change are:

1. Orientation - Dilation preserve orientation

2. Angles - Dilation preserves the interior angles of the figure.

So, the transformation that will preserve both orientation and angles will be used to prove triangles similarity using AA postulate.

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

A translation only moves the entire figure and thus we can overlap the vertices of the triangle and find whether the angles are congruent or not.

With the translation we will prove that other pair of angles of the triangles are congruent and thus the two triangles can be proved similar using the AA similarity postulate.