8-1 The Pythagorean Theorem and Its Converse.

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The Pythagorean Theorem is probably the most famous mathematical relationship. As you learned in Lesson 1-6, it states that in a right triangle, the sum.

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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 Theorem

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.

The hypotenuse of a right triangle has length 12. One leg has length 6. What is the length of the other leg? 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 Triangle A 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?