**Keywords & Theorems**

- Line of Symmetry
- A line that passes through a figure such that it splits the figure into two congruent halves.

- Line Symmetry
- When a figure has one or more lines of symmetry.

- Rotational Symmetry
- When a figure can be rotated (less that ) and it looks the same way it did before the rotation.

- Center of Rotation
- The point at which the figure is rotated around such that the rotational symmetry holds. Typically, the center of rotation is the center of the figure.

- angle of rotation
- The angle of rotation, tells us how many degrees we can rotate a figure so that it still looks the same.

- Transformation
- An operation that moves, flips, or changes a figure to create a new figure.

- Rigid Transformation
- A transformation that preserves size and shape.

- Translation
- A transformation that moves every point in a figure the same distance in the same direction.

- Vector
- A quantity that has direction and size.

- Reflection
- A transformation that turns a figure into its mirror image by flipping it over a line.

- Line of Reflection
- The line that a figure is reflected over.

- Reflection over the axis
- If is reflected over the axis, then the image is .

- Reflection over the axis
- If is reflected over the axis, then the image is .

- Reflection over
- If is reflected over the vertical line , then the image is .

- Reflection over
- If is reflected over the horizontal line , then the image is .

- Reflection over
- If is reflected over the line , then the image is .

- Reflection over
- If is reflected over the line , then the image is .

- Rotation
- A transformation by which a figure is turned around a fixed point to create an image.

- Center of Rotation
- The fixed point that a figure is rotated around.

- Rotation of
- If is rotated around the origin, then the image will be .

- Rotation of
- If is rotated around the origin, then the image will be .

- Rotation of
- If is rotated around the origin, then the image will be .

- Composition (of transformations)
- To perform more than one rigid transformation on a figure.

- Glide Reflection
- A composition of a reflection and a translation. The translation is in a direction parallel to the line of reflection.

- Reflections over Parallel Lines Theorem
- If you compose two reflections over parallel lines that are units apart, it is the same as a single translation of units.

- Reflection over the Axes Theorem
- If you compose two reflections over each axis, then the final image is a rotation of of the original.

- Reflection over Intersecting Lines Theorem
- If you compose two reflections over lines that intersect at , then the resulting image is a rotation of , where the center of rotation is the point of intersection.

- Tessellation
- A tiling over a plane with one or more figures such that the figures fill the plane with no overlaps and no gaps.

## Review Questions

Match the description with its rule.

- Reflection over the axis - A.
- Reflection over the axis - B.
- Reflection over - C.
- Reflection over - D.
- Reflection over - E.
- Reflection over - F.
- Rotation of - G.
- Rotation of - H.
- Rotation of - I.
- Rotation of - J.

## Texas Instruments Resources

*In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9697.*

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## Date Created:

Feb 22, 2012## Last Modified:

Dec 11, 2014
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