http://www.youtube.com/watch?v=CAkMUdeB06o

8-1 The Pythagorean Theorem and Its

Converse

The Pythagorean Theorem

• Named after Pythagoras, a Greek mathematician who lived in 500s BC• Although Pythagoras discovered this

theorem, the Babylonians, Egyptians, and Chinese were aware of this before

The Pythagorean TheoremIf a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Formula:

Pythagorean Triple: a set of nonzero whole numbers a, b, and c that satisfy the equation

Examples:3, 4, 5 8, 15, 175, 12, 13 7, 24, 25

Problem 1: Finding the Length of the Hypotenuse

The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse? Do the side lengths form a Pythagorean triple?

Problem 2: Finding the Length of a Leg

What is the value of x? Express your answer in simplest radical form.

Problem 3: Finding Distance

Dog agility courses often contain a seesaw obstacle, as shown. To the nearest inch, how far above the ground are the dog’s paws when the seesaw is parallel to the ground

Converse of the Pythagorean Theorem

If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side then the triangle is a right triangle.

Problem 4: Identifying a Right Triangle

A triangle has side lengths 85, 84, and 13. Is the triangle a right triangle?

A triangle has side lengths 16, 48, and 50. Is the triangle a right triangle?

Problem 5: Classifying a TriangleA triangle has side lengths 6, 11, and 14. Is it acute, obtuse, or right?

A triangle has side lengths 7, 8, and 9. Is it acute, obtuse, or right?