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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
222 cba
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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