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Bhaskara Proof

http://www.geom.uiuc.edu/%7Edemo5337/Group3/Bp.gif
Looking at the diagram, the figure is made up of a small square, four right triangles, and a large square. The steps for the proof:

• The area of the large square = (c)(c) = c^2.
• The area of the 4 triangles = 4(.5ab) = 2ab.
• The area of the small square = (b - a)(b - a) = b^2 - 2ab + a^2.
• The area of the large square equals the area of four right triangles plus the area of the small square.
  c^2 = (2ab) + (b^2 - 2ab + a^2)
  c^2 = b^2 + a^2

Choupei Proof

http://www.geom.uiuc.edu/%7Edemo5337/Group3/Cp.gif
Looking at the diagram, the figure is made up of a large square, small square, and four right triangles. The steps for solving the proof:

• The area of the large square = (a + b)(a + b) = a^2 + 2ab + b^2.
• The area of the small square = (c)(c) = c^2.
• The area of the four triangles = 4(.5ab) = 2ab.
• The area of large square - area of 4 triangles = area of the small square (a^2 + 2ab + b^2) - (2ab) = c^2
  a^2 + b^2 = c^2
• Therefore, the sum of the squares of the sides of a right triangle equals the square of the hypotenuse.

http://www.cut-the-knot.org/pythagoras/index.shtml

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