7-2 the pythagorean theorem and its converse
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7-2 The Pythagorean Theorem and Its Converse. Goal 1: To use the Pythagorean Theorem Goal 2: To use the Converse of the Pythagorean Theorem. - PowerPoint PPT PresentationTRANSCRIPT
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7-2 The Pythagorean Theorem and Its ConverseGoal 1: To use the Pythagorean Theorem
Goal 2: To use the Converse of the Pythagorean Theorem
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The well-known right triangle relationship called the Pythagorean Theorem is named for Pythagoras, a Greek mathematician who lived in the sixth century b.c. We now know that the Babylonians, Egyptians, and Chinese were aware of this relationship before its discovery by Pythagoras.
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The Pythagorean TheoremIn 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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A Pythagorean triple is a set of nonzero whole numbers a, b, and c that satisfy the equation a2 + b2 = c2. Here are some common Pythagorean triples.
3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25
If you multiply each number in a Pythagorean triple by the same whole number, the three numbers that result also form a Pythagorean triple.
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You can use the Converse of the Pythagorean Theorem to determine whether a triangle is a right triangle.
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Converse of the Pythagorean Theorem
If the square of the length of one 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.
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Theorem: If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse.
If c2 > a2 + b2, the triangle is obtuse.
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Theorem: 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, the triangle is acute.
If c2 < a2 + b2, the triangle is acute.
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Assignment: pp. 360-1 #1-35