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Section 8-1: The Pythagorean Theorem and its Converse

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To use the Pythagorean Theorem. To use the converse of the Pythagorean Theorem.

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Pythagorean Triple

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Greek mathematician from the 6 th century BC. Famous for the Pythagorean Theorem Others knew of the Pythagorean Theorem first: Babylonians Egyptians Chinese

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In a right triangle, the sum of the squares of the lengths of the legs is equal to the square 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:

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Solve for the variable. Do the sides of the triangle form a Pythagorean triple? 21 20 x

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Solve for the variable. Do the sides of the triangle form a Pythagorean triple? 16 34 y

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Solve for the variable. Do the sides of the triangle form a Pythagorean triple? 4 8 z

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If the square of the lengths 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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Is the triangle a right triangle? 6 10 8

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Is the triangle a right triangle? 6 2 5

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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, then the triangle is obtuse.

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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 obtuse.

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7, 8, and 11 16, 19, and 24 5, 7, and 10

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