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Section 8-3

Section 8-3. The Converse of the Pythagorean Theorem. Theorem 8-3. If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. Examples:.

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Section 8-3

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  1. Section 8-3 The Converse of the Pythagorean Theorem

  2. Theorem 8-3 • If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

  3. Examples: • Determine if the given measures are measures of the sides of a right triangle. • 14, 48, 50 • 50, 75, 85 • 15, 36, 39 • 45, 60, 80 Yes No Yes No

  4. Some Common Right Triangle Lengths: • 3, 4, 5 • 5, 12, 13 • 8, 15, 17 • 7, 24, 25

  5. Theorem 8-4: If , then and is acute Example:

  6. Theorem 8-5: If , then and is obtuse Example:

  7. Examples: Classify each triangle with sides of the given lengths as acute, right, or obtuse. • 5, 12, 14 • 6, 7, 8 • 1, 3, Obtuse Acute Acute Right

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