Sunday, August 17, 2014
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| The Pythagorean Theorem |
Start with a cutout of a right triangle.
Cut three more cutouts.
Let us name the sides of the right triangle with c as the hypotenuse.
Now, let us form a square using the four (4) triangles. This time, use the hypotenuse as the sides of the square.
Let us take a look at the different parts of the square we formed. If we separate the whole square, we can get its area in terms of c.
The middle part is also a square with sides equal to the difference of sides b and a. The area can be obtained as
On the other hand, the area of the four triangles outlining the sides of the whole square is as follows.
Combining their areas, we obtain
Thus, c^2 = a^2 + b^2.
Your questions, comments and suggestions are welcome here. Kindly write them in the comment box below.
This is a great follow-up to the first Pythagorean Theorem exploration. I like how the geometric approach encourages students to look at the theorem from a different perspective instead of treating it as just a formula to memorize. Visual reasoning like this can make the relationship between the legs and hypotenuse much easier to understand, especially when students are first learning right-triangle geometry. I’ve also found it useful to have a simple tool for checking these calculations while practicing: https://pythagorastheoremcalculation.co/
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