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8.1 The Pythagorean Theorem and Its Converse

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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

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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

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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.

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Practice #1 The hyp of a right triangle is 12 m and the leg is 5 m. Find the length of the other leg.

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Practice #2 The legs of a right triangle are 10 ft. and 8 ft. Find the length of the hypotenuse.

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Practice #3 The hypotenuse of an isosceles right triangle is 18 mi. long. Find the lengths of both legs

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Simplify #1 √12

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Simplify #2 √150

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Homework/Classwork Pgs 420-421 #2-28e, 36-46e

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