**Warmup**

**Activity #1**

**Explore Transformation, Rotation, & Reflection in the Coordinate Plane.**

- 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 .

- 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.

- 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.

**Activity #2**

**Explore More Translation, Rotation, & Reflection in the Coordinate Plane.**

- Translate the shape so that A goes to A’ .

- Rotate the shape 180 degrees counterclockwise around B.

- Reflect the shape over the line shown.

**Activity #3**

**Explore 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______________________.

(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.

(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 vertex/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.

**Challenge #1**

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

Explain how you know.

**Challenge #2**

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?

**Challenge #3**

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.

**Quiz Time**

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