Pythagorean Theorem

Definition

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides.

5 Must Know Facts For Your Next Test

1. The theorem only applies to right triangles.
2. It can be used to determine whether a triangle is a right triangle by checking if \(a^2 + b^2 = c^2\).
3. The theorem is fundamental for trigonometric calculations involving right triangles.
4. It forms the basis for distance calculations in coordinate geometry.
5. Pythagoras, an ancient Greek mathematician, is credited with its discovery.

Review Questions

• What type of triangle does the Pythagorean Theorem apply to?
• How do you express the Pythagorean Theorem algebraically?
• Can you use the Pythagorean Theorem to verify if a given set of lengths form a right triangle?

Related terms

Hypotenuse:

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

Legs: The two shorter sides of a right triangle that form the right angle.

Right Angle: An angle measuring exactly 90 degrees, forming part of a right triangle.