Luv4eva24
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A triangle is dilated by scale factor of 1/5 in a rotated night degrees clockwise about the origin why is the image similar to the pre image

Sagot :

sqdancefan

9514 1404 393

Answer:

  conditions for similarity are not violated by the transformation

Step-by-step explanation:

Dilation changes linear measures proportionally, and has no effect on angles. Rotation changes neither lengths nor angles. Hence the dilated, rotated triangle has the same angles as the original, and has proportional side lengths. Those are the requirements for figures to be similar, so the triangles are similar.

kylanseago

Answer:

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 :)

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