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**Exploring Transformation, Rotation, & Reflection in the coordinate plane.**

**(A).** Translate Polygon **A** so point** P** goes to point **P’**. In the image, write in the length of each side in grid units using the pen tool .

**(B).** Rotate Triangle B 90 degrees clockwise using R as the center of rotation. In the image, write the measure of each angle in its interior using the pen tool.

**(C).** Reflect Pentagon C across l line . In the image, write the length of each side and the measure of each interior angle, in grid units, next to the corresponding side or angle.

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**Exploring More Translation, Rotation, & Reflection in the coordinate plane.**

**(A).** Translate the shape so that A goes to A’ .

**(B).** Rotate the shape 180 degrees counterclockwise around B.

**(C).** Reflect the shape over the line shown.

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**Exploring Rigid Transformations of Polygons.**

**Rigid Transformation – A transformation that does not alter the size or shape of a figure.**

Use your exploration with the dynamic features of the applets in order to complete all of the blanks for each transformation below.

Observe the relationship between the side lengths of the original and the image. Observe the relationship between the angles of the original and the image.

(1). A **translation** of an object is a _________________________ transformation because it keeps the same shape and size of the original, but changes its __________________ . The image of a translated shape has angles and side lengths that are ____________________ to the corresponding angles and side lengths of the pre-image (original shape). The vector (or rule – direction and length) moves all the vertices and sides the same______________________.

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(2). A **reflection** of an object is a _________________________ transformation because it keeps the same shape and size of the original, but changes its __________________ and _____________ it. The image of a reflected shape has angles and side lengths that are ____________________ to the corresponding angles and side lengths of the pre-image (original shape). The line of reflection is the ______________________ of the segments that connect corresponding vertices.

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(3). A** rotation** of an object is a _________________________ transformation because it keeps the same shape and size of the original, but changes its __________________ and ______________it. The image of a rotated shape has angles and side lengths that are ____________________ to the corresponding angles and side lengths of the pre-image (original shape). The angle of rotation moves each vertice/side of the pre-image around a given point of rotation the given amount degrees __________ or_________ so that the angle between corresponding vertices is ________________to the angle of rotation

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Is there a rigid transformation taking Rhombus P to Rhombus Q?

Explain how you know.

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A square is made up of an L-shaped region and three transformations of the region.

If the perimeter of the square is 40 units, what is the perimeter of each L-shaped region?

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Here is a grid showing triangle ABC and two other triangles. You can use a rigid transformation to take triangle ABC to one of the other triangles.

(1). Which one? Explain how you know.

(2). Describe a rigid transformation that takes triangle ABC to the triangle you selected.

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