Pythagorean Theorem

Geometry
rule

Also known as: a² + b² = c², right triangle theorem

Grade 6-8

View on concept map

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Essential for distance, navigation, and countless applications.

Definition

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

💡 Intuition

If you draw squares on each side of a right triangle, the two smaller squares fill the big one exactly.

🎯 Core Idea

A fundamental relationship between sides of right triangles.

Example

Sides 3 and 4: 3^2 + 4^2 = 9 + 16 = 25 = 5^2, so the hypotenuse is 5.

Formula

a^2 + b^2 = c^2 (c is the hypotenuse)

Notation

a, b are the legs; c is the hypotenuse (longest side, opposite the right angle)

🌟 Why It Matters

Essential for distance, navigation, and countless applications.

💭 Hint When Stuck

Ask yourself: which side is across from the 90-degree angle? Label that one c, then plug the other two into a-squared plus b-squared.

Formal View

In \triangle ABC with \angle C = 90°: |AB|^2 = |AC|^2 + |BC|^2, equivalently c^2 = a^2 + b^2 where c = |AB|

🚧 Common Stuck Point

c must be the longest side (hypotenuse), opposite the right angle.

⚠️ Common Mistakes

  • Using wrong side as hypotenuse
  • Forgetting to take square root for final answer

Frequently Asked Questions

What is Pythagorean Theorem in Math?

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Why is Pythagorean Theorem important?

Essential for distance, navigation, and countless applications.

What do students usually get wrong about Pythagorean Theorem?

c must be the longest side (hypotenuse), opposite the right angle.

What should I learn before Pythagorean Theorem?

Before studying Pythagorean Theorem, you should understand: triangles, exponents, square roots.

How Pythagorean Theorem Connects to Other Ideas

To understand pythagorean theorem, you should first be comfortable with triangles, exponents and square roots. Once you have a solid grasp of pythagorean theorem, you can move on to distance formula and trigonometric functions.

← Back to Explorer

Interactive Playground

Interact with the diagram to explore Pythagorean Theorem