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Published byJanel Patterson Modified over 8 years ago

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8-1 The Pythagorean Theorem and Its Converse

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Parts of a Right Triangle In a right triangle, the side opposite the right angle is called the hypotenuse. – It is the longest side. The other two sides are called the legs.

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The Pythagorean Theorem Pythagorean Theorem: If 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. a 2 + b 2 = c 2

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Pythagorean Triples A Pythagorean triple is a set of nonzero whole numbers that satisfy the Pythagorean Theorem. Some common Pythagorean triples include: 3, 4, 55, 12, 138, 15, 177, 24, 25 – If you multiply each number in the triple by the same whole number, the result is another Pythagorean triple!

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Finding the Length of the Hypotenuse What is the length of the hypotenuse of ABC? Do the sides form a Pythagorean triple?

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

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Finding the Length of a Leg What is the value of x? Express your answer in simplest radical form.

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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.

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Triangle Classifications Converse of the Pythagorean Theorem: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. – If c 2 = a 2 + b 2, than ABC is a right triangle. Theorem 8-3: If the square of the length of the longest side of a triangle is great than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse. – If c 2 > a 2 + b 2, than ABC is obtuse. Theorem 8-4: If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is acute. – If c 2 < a 2 + b 2, than ABC is acute.

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Classifying a Triangle Classify the following triangles as acute, obtuse, or right. – 85, 84, 13 – 6, 11, 14 – 7, 8, 9

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