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The Pythagorean Theorem and Its Converse

The Pythagorean Theorem and Its Converse. OBJECTIVE: To use the Pythagorean Theorem and its converse BIG IDEAS: MEASUREMENT REASONING AND PROOF ESSENTIAL UNDERSTANDINGS:

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The Pythagorean Theorem and Its Converse

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  1. The Pythagorean Theorem and Its Converse OBJECTIVE: To use the Pythagorean Theorem and its converse BIG IDEAS: MEASUREMENT REASONING AND PROOF ESSENTIAL UNDERSTANDINGS: If the lengths of any two sides of a right triangle are known, the length of the third side can be found using the Pythagorean Theorem. If the lengths of all sides of a triangle are known, it can be determined whether the triangle is acute, right or obtuse. MATHEMATICAL PRACTICE: Make sense of problems and persevere in solving them

  2. Introduction • The Pythagorean Theorem was one of the first theorems used by mathematicians in early civilizations. Although named after and credited to the Greek mathematician Pythagoras because of his proof of the theorem, the notation of the theorem actually dates back to a millennium earlier, when it was first used by the Babylonians.

  3. Pythagorean Theorem • If a triangle is a _______________ triangle, then the _______________ of the squares of the lengths of the _______________ is equal to the square of the length of the ____________________ • Pythagorean triple: A set of nonzero whole numbers that satisfy the equation

  4. EX 1: Find the length of the hypotenuse of the right triangle. Tell whether the side lengths form a Pythagorean Triple. • A) • B)

  5. EX 2: Find the unknown side length • A) • B)

  6. EX 3: Finding the length of a Leg • A 48 inch wide screen television means that the measure along the diagonal is 48 inches. If the screen is square, what are the dimensions of the length and width? Round to the nearest tenth of an inch.

  7. Converse of the Pythagorean Theorem • If the _______________ of the squares of the lengths of _______________ sides of a triangle is equal to the _______________ of the length of the third side, then the triangle is a _______________ triangle • EX 4: A triangle has side lengths given. Is the triangle a right triangle? Explain • A) 8, 7, and 10 B) 85, 84 and 13

  8. Theorems 9.6 and 9.7 • THEOREM 9.6: • If the _______________ of the length of the ____________________side of the triangle is _______________ than the sum of the squares of the lengths of the other two sides, then the triangle is _______________ • THEOREM 9.7: • If the _______________ of the length of the ____________________side of the triangle is _______________ than the sum of the squares of the lengths of the other two sides, then the triangle is _______________

  9. EX 5: A triangle has the given lengths. Is it acute, obtuse, or right? • A) 58, 69, 80 • B) 11, 30, 39 • C)

  10. The Pythagorean Theorem and Its Converse WS 30 questions

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