Pythagorean theorem, its converse and special right triangles

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Learn it In a right triangle $a^2 + b^2 = c^2$. If the sides of a triangle satisfy this, it is a right triangle (the converse). Special triangles: 45-45-90 has sides in ratio 1 : 1 : √2; 30-60-90 has 1 : √3 : 2.

Example: Is a 9, 12, 15 triangle right-angled?

$9^2 + 12^2 = 81 + 144 = 225$.
$15^2 = 225$.
Equal, so yes.

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