Why can the Pythagorean Theorem only be used with Right Triangles?

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Answer 1 · 2018-04-25T02:05:34

It's not really true. The Pythagorean Theorem (its converse, really) can be used on any triangle to tell us whether or not it is a right triangle.

For example, let's check the triangle with sides 2,3,4: $2^{2} + 3^{2} = 13 \neq 4^{2}$ $2^2+3^2=13 ne 4^2$ so this isn't a right triangle.

But of course $3^{2} + 4^{2} = 5^{2}$ $3^2+4^2=5^2$ so 3,4,5 is a right triangle.

The Pythagorean Theorem is a special case of the Law Of Cosines for $C = 90^{\circ}$ $C=90^circ$ (so $cos C = 0$ $cos C= 0$ ).

$c^{2} = a^{2} + b^{2} - 2 a b cos C$ $c^2 = a^2 + b^2 - 2 a b cos C$