- 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"}}]]
- 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.
- 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.)
[[{"fid":"58","view_mode":"default","type":"media","attributes":{"height":186,"width":234,"class":"media-element file-default"}}]]
- 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.
[[{"fid":"59","view_mode":"default","type":"media","attributes":{"height":200,"width":624,"class":"media-element file-default"}}]]
- 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
[[{"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"}}]]