Pythagorean Theorem

The legs of a right triangle are the two sides that form the right angle, commonly referred to as sides a and b.

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.

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Using the Pythagorean Theorem: $$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$ , so $$c = 5$$ .

The set of sides 5, 12, and 13 can form a right triangle.

To find a missing side, rearrange the Pythagorean Theorem: $$c = \text{sqrt}(a^2 + b^2)$$ for the hypotenuse or $$a = \text{sqrt}(c^2 - b^2)$$ for a leg.

False. The Pythagorean Theorem only applies to right triangles.

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: $$b = \text{sqrt}(10^2 - 6^2) = \text{sqrt}(100 - 36) = \text{sqrt}(64) = 8$$ .