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Problem of the Week #5 – A Fourth and Last Look (for now) at the Pythagorean Theorem

Posted by Jeff Simpson under

All Problems of the Week - And Solutions,

Geometry,

Pythagorean Theorem | Tags:

learning math,

math instruction,

math problems,

teaching math |

1 Comment
To wrap up this series of Pythagorean Problems of the Week, here is one that often presents difficulties for students at first. Where are the numbers?! What is the length of a side that is only assigned a letter!!?

There has been a purposeful flow to our weekly Pythagorean problems. We began with whole number measurements and solutions, the second one using the information to solve another problem, and moved to whole number measurements with an irrational number solution. We now end with a problem that preserves complete generality.

Can you use the “measurements” in these two pictures to prove that a^{2} + b^{2} = c^{2} is true for all right triangles? The length of “a” is the same in both figures, as is the length of “b” and “c.” For this problem, all corners that look square are square. The solution will be posted next week with a special tribute to the scarecrow from the Wizard of Oz.

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