# PROPERTIES OF ROTATIONS WORKSHEET

## About "Properties of rotations worksheet"

Properties of rotations worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on rotations.

## Properties of rotations

The following are the three basic properties of reflections :

1.  A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.

2.  A rotation preserves lengths of segments.

3.  A rotation preserves measures of angles.

When parallel lines are rotated, their images are also parallel. A line is only parallel to itself when rotated exactly 180°.

## Properties of rotations worksheet - Problems

1.  The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° counterclockwise about the origin and determine whether image and pre-image of the rotated object satisfy the properties.

2.  The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° clockwise about the origin and determine whether image and pre-image of the rotated object satisfy the properties.

## Properties of rotations worksheet - Solution

Problem 1 :

The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° counterclockwise about the origin and determine whether image and pre-image of the rotated object satisfy the properties.

Solution :

Step 1 :

Trace triangle xyz and the x- and y-axes onto a piece of paper.

Step 2 :

Rotate your triangle 90° counterclockwise about the origin. The side of the triangle that lies along the x-axis should now lie along the y-axis.

Step 3 :

Sketch the image of the rotation. Label the images of points X, Y, and Z as X', Y', and Z'.

Step 4 :

The rotation done above maps each side to its corresponding side and each angle to its corresponding angle. And also, the rotation preserves lengths of segments and measures of angles. So, the rotation done above satisfies the properties.

Problem 2 :

The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° clockwise about the origin and determine whether image and pre-image of the rotated object satisfy the properties.

Solution :

Step 1 :

Trace triangle xyz and the x- and y-axes onto a piece of paper.

Step 2 :

Rotate your triangle 90° clockwise about the origin. The side of the triangle that lies along the x-axis should now lie along the y-axis.

Step 3 :

Sketch the image of the rotation. Label the images of points X, Y, and Z as X", Y", and Z".

Step 4 :

The rotation done above maps each side to its corresponding side and each angle to its corresponding angle. And also, the rotation preserves lengths of segments and measures of angles. So, the rotation done above satisfies the properties.

After having gone through the stuff given above, we hope that the students would have understood "Rotations".

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