The Converse of the Pythagorean Theorem

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7.2 Converse of Pythagorean Theorem

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Presentation transcript:

The Converse of the Pythagorean Theorem Section 9-3 The Converse of the Pythagorean Theorem

Recall: The sum of the two smaller measures must be greater than the largest measure in order for a triangle to exist.

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 other two sides, then the triangle is a right triangle.

a b c C A B If , then is a right triangle.

Theorem 9-6 If the sum of the squares of the length of the two shorter sides is greater than the square of the length of the longest side, then the triangle is acute.

If , then the triangle is an acute triangle.

Theorem 9-7 If the sum of the squares of the length of the two shorter sides is less than the square of the length of the longest side, then the triangle is obtuse.

If , then the triangle is an obtuse triangle.