8.1 The Pythagorean Theorem and Its Converse

Pythagorean Theorem

• In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse

Pythagorean triple

• Pythagorean triple – a set of nonzero whole numbers a, b, and c that satisfy the equation

• 3,4,5• 5,12,13• 8,15,17• 7,24,25

222 cba

Converse of the Pythagorean Theorem

• What if a²+b² ≠ c²? Then what kind of triangle is formed?

• Acute Triangle: if c² < a² + b²

• Obtuse Triangle: if c² > a² + b²

• These two facts need to be memorized for the test.• Don’t forget if c² = a² + b² then the triangle is a Right

Triangle.

Practice #1

• The hyp of a right triangle is 12 m and the leg is 5 m. Find the length of the other leg.

Practice #2

• The legs of a right triangle are 10 ft. and 8 ft. Find the length of the hypotenuse.

Practice #3

• The hypotenuse of an isosceles right triangle is 18 mi. long. Find the lengths of both legs

Simplify #1

• √12

Simplify #2

• √150

Homework/Classwork

• Pgs 420-421 #2-28e, 36-46e