The Pythagorean Theorem and Its Converse

Pythagorean Theorem

In a right Triangle with legs a and b and hypotenuse c:

a² + b² = c²

Finding a Missing Side

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

Pythagorean Triples

Sets of three positive integers that satisfy a² + b² = c²:

• 3, 4, 5 (and multiples: 6, 8, 10; 9, 12, 15...)
• 5, 12, 13
• 8, 15, 17
• 7, 24, 25

Converse of the Pythagorean Theorem

• If a² + b² = c²: the Triangle is right.
• If a² + b² > c²: the Triangle is acute.
• If a² + b² < c²: the Triangle is obtuse.