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Triangle Transformation

Age 7 to 14 Challenge Level:
 

Draw a triangle on a piece of paper, and cut it out.

Can you find a way to cut your triangle into no more than four pieces, and reassemble the pieces to make a rectangle?

Is it always possible, no matter what triangle you start with?






If you don't know where to start, click below to see some prompts that may help you:


First prompt:

Start with an isosceles triangle. How could you make it into a rectangle?
Is there a relationship between the base and height of your triangle, and the base and height of the rectangle?


Second prompt:

Draw any triangle, find the midpoints of two of the sides, and join them together. What do you notice?


Third prompt:

Once you have joined the midpoints, can you rearrange the pieces to make a parallelogram? Does that help you to create a rectangle?