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pogonyaev
3 years ago
12

A triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin. Why is the image similar t

o the pre-image? Check all that apply.
A) The corresponding sides of the triangles are congruent.
B) The corresponding angles of the triangles are congruent.
C) The corresponding sides of the image are 5 times as long as those of the pre-image.
D) The image is a reduction of the pre-image.
E) Neither the dilation nor the rotation change the shape of the triangle.
F) The rotation reduces the size of the triangle.
Mathematics
2 answers:
DerKrebs [107]3 years ago
4 0

Answers:

<em>B.The corresponding angles of the triangles are congruent </em>

<em>D.The image is a reduction of the pre-image </em>

<em>E. Neither the dilation nor the rotation change the shape of the triangle</em>

yan [13]3 years ago
3 0
<u><em>Answers:</em></u>
The corresponding angles of the triangles are congruent
The image is a reduction of the pre-image
Neither the dilation nor the rotation change the shape of the triangle

<u><em>Explanation:</em></u>
<u>For shapes to be similar:</u>
1- there should be a ratio between the sides
2- angles in first shape should be congruent to angles in second shape

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

<u>Let's check the choices:</u>
<u>1- </u><span><u>The corresponding sides of the triangles are congruent:</u>
This option is incorrect as dilation changes the lengths of the sides

<u>2- </u></span><span><u>The corresponding angles of the triangles are congruent:</u>
This option is correct as neither dilation nor rotation alters the measures of the angles

<u>3- </u></span><span><u>The corresponding sides of the image are 5 times as long as those of the pre-image:</u>
This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image

<u>4- </u></span><span><u>The image is a reduction of the pre-image:</u>
This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced

<u>5- </u></span><span><u>Neither the dilation nor the rotation change the shape of the triangle:</u>
This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)

<u>6- </u></span><u>The rotation reduces the size of the triangle:</u>
This option is incorrect as rotation does not alter the size of the shape. It only changes its position

Hope this helps :)

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