Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: $$a^2 + b^2 = c^2$$ .

The Pythagorean Theorem ONLY works on right triangles.

The longest side of a right triangle is called the hypotenuse.

Using the Pythagorean Theorem: $$3^2 + 4^2 = c^2$$ , so $$9 + 16 = c^2$$ , thus $$c = 5$$ .

Using the Pythagorean Theorem: $$6^2 + b^2 = 10^2$$ , so $$36 + b^2 = 100$$ , thus $$b = 8$$ .

The formula to find the hypotenuse (c) is: $$c = \text{sqrt}(a^2 + b^2)$$ .

Using the Pythagorean Theorem: $$5^2 + b^2 = 13^2$$ , so $$25 + b^2 = 169$$ , thus $$b = 12$$ .

The relationship is that the sum of the squares of the two legs equals the square of the hypotenuse: $$a^2 + b^2 = c^2$$ .

Using the Pythagorean Theorem: $$8^2 + 15^2 = c^2$$ , so $$64 + 225 = c^2$$ , thus $$c = 17$$ .

A right triangle is a triangle that has one angle measuring 90 degrees.