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The right-triangle or the right-angled-triangle, meaning a triangle that has as one of its angels, the angle 90o.

His famous theorem is that

"the sum of the squares of the length of the two sides forming the right-angle is equal to the square of the length of the side opposite the right-angle"

It is better put as

h2 = a2 + b2

where

h = hypotenuse (the side opposite the right-angle) and

a = one of the two sides making the right-angle and

b = the other of the two sides making the right-angle

What he found far more interesting was the property of some specific examples of this triangle, e.g.

A triangle with sides 3 and 4 would have a hypotenuse of 5

i.e. 32 + 4 2 = 5 2 (9 + 16 = 25)

He further found that any right-angled triangle that had whole multiples of these sides followed the same pattern; e.g:

A right-triangle with sides of 6 and 8 would have a hypotenuse of 10 (36 + 64 = 100),

A right triangle with sides of 9 and 12 would have a hypotenuse of 15 (81 + 144 = 225)

A right-triangle with sides of 12 and 16 would have a hypotenuse of 20 (144 + 256 = 400)

and so on

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12y ago

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