Common Core: High School - Geometry

Explore the principles and applications of geometry, including shapes, theorems, and real-world problem-solving.

Advanced Topics

The Pythagorean Theorem

Discovering the Pythagorean Theorem

The Pythagorean Theorem is a legendary result in geometry that connects the sides of a right triangle.

The Theorem

In any right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse):

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

Where \(a\) and \(b\) are the lengths of the legs, and \(c\) is the hypotenuse.

Applying the Theorem

This theorem helps us find distances, heights, and even the shortest path between two points!

Why It’s Important

The Pythagorean Theorem is used in navigation, construction, and design—whenever you need to measure or build something with right angles.

Key Formula

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

Examples

  • Finding the diagonal length of a TV screen.

  • Calculating the shortest route across a rectangular park.

In a Nutshell

A powerful tool for finding missing sides in right triangles.