In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
Thus, if the hypotenuse, the side opposite the right angle, has length c and the other two sides have lengths a and b, then a2 + b2 = c2. One elegant proof is obtained by dividing up a square of side a + b in two different ways as shown in the figure, and equating areas.
Triangles leave area c2
Triangles leave area a2 + b2
Pythagoras’s Theorem is a special case of the cosine rule.
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