No Bending or Stretching

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