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 is expressed as: $$c^2 = a^2 + b^2$$ .

The Pythagorean Theorem ONLY works on right triangles.

Using the Pythagorean Theorem: $$c^2 = 6^2 + 8^2 = 36 + 64 = 100$$ , so $$c = \text{10 cm}$$ .

The formula is $$c^2 = a^2 + b^2$$ , where c is the hypotenuse and a and b are the other two sides.

Using the Pythagorean Theorem: $$c^2 = a^2 + b^2$$ , we have $$13^2 = 12^2 + b^2$$ . Thus, $$169 = 144 + b^2$$ , so $$b^2 = 25$$ , and $$b = 5 in$$ .

Using the Pythagorean Theorem: $$c^2 = 9^2 + 12^2 = 81 + 144 = 225$$ , so $$c = 15 cm$$ .

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

Using the Pythagorean Theorem: $$c^2 = 5^2 + 12^2 = 25 + 144 = 169$$ , so $$c = 13 cm$$ .

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using the Pythagorean Theorem: $$10^2 = 6^2 + b^2$$ , so $$100 = 36 + b^2$$ , thus $$b^2 = 64$$ , and $$b = 8 cm$$ .