Pythagoras Theorem – A Visual Proof(A)

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We have 2 squares in which 4 right angled triangles of the same size have been arranged.

The sides of each of these squares is a + b.

In each of the triangles a & b are the 2 sides adjacent to the right angle and c is the hypotenuse.

We have to prove Pythagoras Theorem which states that a^2 + b^2 = c^2.

We will prove that the sum of the areas of a square with side a (a*2) and a square with side b(b^2) would be equal to the area of a square with side c.

In the first square, the 4 triangles have been arranged along the 4 sides thus leaving an empty space which is a square with side c.

In the second square a pair of right angles have been combined to form a rectangle. Both the rectangles have been arranged touching 2 opposite corners of the square. This leaves 2 empty squares in the middle; one with side a and the other with side b.

In both cases the bigger squares have the same area. The 4 rectangles have been arranged inside the square.

Hence the area of the empty square left in both cases must be equal!

Hence a^2 + b^ 2 = C^2.

< 23.7 Pythagoras Theorem | Topic Index | 23.9 Quadrilaterals >