The document contains proofs of the Pythagorean theorem and similarity using triangles. It first shows the theorem can be proven by decomposing a right triangle into four equal triangles and relating their areas. It then presents a second proof using the areas of a large square formed by the hypotenuse and legs, the total area of the four triangles, and the area of the shaded region inside the large square but outside the triangles. This relationship leads to the Pythagorean equation a2 + b2 = c2.
4. 17.notebook October 09, 2012
Area of each triangle = 1/2bh Area of all 4 triangles = 4(1/2)ab = 2ab
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5. 17.notebook October 09, 2012
Area of shaded = c2
Area of large square = (a + b)2
Area of shaded = large square area of triangles
c2 = (a + b)2 2ab
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