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- PYTHAGOREAN THEOREM (Exploration 2)

Sunday, August 17, 2014

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.

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