△ The Pythagorean Theorem

The Theorem

In a right triangle with legs a and b and hypotenuse c: a² + b² = c².

The hypotenuse is always opposite the right angle and is always the longest side.

Finding Missing Sides

• Find c: c = √(a² + b²)
• Find a: a = √(c² − b²)
• Find b: b = √(c² − a²)

Pythagorean Triples

Sets of integers that satisfy a² + b² = c²: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Multiples also work: 6-8-10, 9-12-15, etc.

Converse Theorem

If a² + b² = c², the triangle is right. If a² + b² > c², it's acute. If a² + b² < c², it's obtuse.