8th Grade Math

Algebra foundations, geometry, and mathematical modeling for eighth grade students.

Advanced Topics

Pythagorean Theorem

What Is the Pythagorean Theorem?

The Pythagorean Theorem is a rule for right triangles. It says that the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.

The Formula

For any right triangle with sides \(a\), \(b\), and hypotenuse \(c\):

\[ a^2 + b^2 = c^2 \]

Why Does It Matter?

This theorem helps you find missing side lengths in real life—like the shortest path across a field or the length of a ladder leaning against a wall.

Try It Out

Draw a right triangle and check the theorem for yourself!

Key Formula

\[a^2 + b^2 = c^2\]

Examples

  • If a triangle has sides 3 and 4, the hypotenuse is \(c = \sqrt{3^2 + 4^2} = 5\).

  • A ramp with a base of 6 ft and height of 8 ft has a length of 10 ft.

In a Nutshell

The Pythagorean Theorem relates the sides of a right triangle.