1. 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.

[[{"fid":"56","view_mode":"default","type":"media","attributes":{"height":237,"width":488,"class":"media-element file-default"}}]]

1. Use pictures and words to describe where you decided to cut (a cut can be represented by a dotted line [[{"fid":"57","view_mode":"default","type":"media","attributes":{"height":32,"width":30,"class":"media-element file-default"}}]]) and how you rearranged the pieces.

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

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

1. 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.)

[[{"fid":"58","view_mode":"default","type":"media","attributes":{"height":186,"width":234,"class":"media-element file-default"}}]]

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

1. 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.

[[{"fid":"59","view_mode":"default","type":"media","attributes":{"height":200,"width":624,"class":"media-element file-default"}}]]

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

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

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

1. 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

[[{"fid":"60","view_mode":"default","type":"media","attributes":{"height":327,"width":672,"class":"media-element file-default"}}]]

[[{"fid":"61","view_mode":"default","type":"media","attributes":{"height":399,"width":504,"class":"media-element file-default"}}]]

Problem 2

[[{"fid":"62","view_mode":"default","type":"media","attributes":{"height":215,"width":672,"class":"media-element file-default"}}]]

© 2008 by Education Development Center, Inc. from The Fostering Geometric Thinking Toolkit. Portsmouth, NH: Heinemann. Reproduced with permission.