Archive for August 2014

PYTHAGOREAN THEOREM (Exploration 2)

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The Pythagorean Theorem
Here is another proof for the Pythagorean Theorem. You can see the first part here.
Start with a cutout of a right triangle.
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Cut three more cutouts.
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Let us name the sides of the right triangle with c as the hypotenuse.
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Now, let us form a square using the four (4) triangles. This time, use the hypotenuse as the sides of the square.
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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.
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The middle part is also a square with sides equal to the difference of sides b and a. The area can be obtained as
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On the other hand, the area of the four triangles outlining the sides of the whole square is as follows.
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Combining their areas, we obtain
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Thus, c^2 = a^2 + b^2.

Your questions, comments and suggestions are welcome here. Kindly write them in the comment box below.

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