- Find a way to cut this parallelogram into pieces you can rearrange to form a rectangle (final page of this problem contains a copy for you to cut). Be sure to use all of the pieces when creating the rectangle.

- Use pictures and words to describe where you decided to cut (a cut can be represented by a dotted line ) and how you rearranged the pieces.

- List the properties of the parallelogram that changed and properties that stayed the same when you changed it into a rectangle.

- How can you be sure your final shape has the properties of a rectangle? Write a convincing mathematical explanation.

- Will your method work for a parallelogram that looks like this? If not, what changes do you need to make in the description of your method? (There is a larger replica of this shape attached.)

- Will your method allow you to transform any parallelogram into a rectangle? Explain.

- Find a way to cut the rectangle below into pieces you can rearrange to form a right triangle (final page of this problem contains a copy of this rectangle for you to cut). Be sure to use all of the pieces when creating the right triangle.

- Use pictures and words to describe where you decided to cut and how you rearranged the pieces.

- List the properties of the rectangle that changed and properties that stayed the same when you changed it into a triangle.

- How can you be sure your final shape has the properties of a right triangle? Write a convincing mathematical explanation.

- Will your method allow you to transform any rectangle into a right triangle? Explain.

## Extension

You already cut a parallelogram into pieces you rearranged to form a rectangle. Can you cut a parallelogram into pieces you can rearrange to form other shapes? What other shapes can you form?

How could you dissect a parallelogram and rearrange its pieces to form a right triangle? Use pictures and words to describe where to cut and how to rearrange the pieces.

**Shapes Templates**

Problem 1

Problem 2