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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 to 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.

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Louli
Answers:
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

Explanation:
For shapes to be similar:
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

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

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

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

4- The image is a reduction of the pre-image:
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

5- Neither the dilation nor the rotation change the shape of the triangle:
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)

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

Hope this helps :)

raphealnwobi

If a triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin, the image similar to the pre-image because:

B) The corresponding angles of the triangles are congruent.

E) Neither the dilation nor the rotation change the shape of the triangle.

Transformation is the movement of an object from an initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If an object its dilated, it is either increased or reduced. Whereas rotation only changes the orientation of the object.

Two objects are similar if they have the same shape and the ratio or their sides are in the same proportion. Hence they have the same angle measure.

Hence if a triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin, the image similar to the pre-image because:

B) The corresponding angles of the triangles are congruent.

E) Neither the dilation nor the rotation change the shape of the triangle.

Find out more at: https://brainly.com/question/13176891

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