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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
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?