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Applying the Pythagorean Theorem and Its Converse 3-9 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes
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Applying the Pythagorean Theorem and Its Converse 3-9 Warm Up Find the distance between each pair of points. 1. (8, 2) and (8, 7) 2. (–2, 4) and (5, 4) 3. (–1, –1) and (9, –1) 4. (–8, –4) and (–2, –4) 5 units 7 units 10 units 6 units
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Applying the Pythagorean Theorem and Its Converse 3-9 Learn to use the Distance Formula and the Pythagorean Theorem and its converse to solve problems.
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Applying the Pythagorean Theorem and Its Converse 3-9 7.615 c Use the Pythagorean Theorem Simplify. 7 2 + 3 2 = c 2 49 + 9 = c 2 58 = c 2 58 = c Add. Example 1: Marketing Application A.What is the diagonal length of the projector screen? The diagonal length should be given as about 7.62 feet.
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Applying the Pythagorean Theorem and Its Converse 3-9 14.42 c Use the Pythagorean Theorem Simplify. 12 2 + 8 2 = c 2 144 + 64 = c 2 208 = c 2 208 = c Add. Check It Out B. What is the diagonal length of the projector screen? The diagonal length should be given as about 14.4 feet. 12 ft 8 ft
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Applying the Pythagorean Theorem and Its Converse 3-9
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Applying the Pythagorean Theorem and Its Converse 3-9 Use the Distance Formula. J and K Example 2: Finding Distance on the Coordinate Plane A. Find the distances between the points to the nearest tenth. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².
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Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Additional Example 2A Continued Find the distances between the points to the nearest tenth. d = (0 – (–4))² + (–3 – 0 )² d = (4)² + (–3)² Simplify powers. d = 16 + 9 The distance between A and B is 5 units.
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Applying the Pythagorean Theorem and Its Converse 3-9 L and M Example 2: Finding Distance on the Coordinate Plane B. Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².
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Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Additional Example 2B Continued Find the distances between the points to the nearest tenth. d = (5 – 4)² + (–3 – 0)² d = (1)² + (–3)² Simplify powers. d = 1 + 9 The distance between L and M is about 3.2 units.
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Applying the Pythagorean Theorem and Its Converse 3-9 J and L Check It Out C. Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².
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Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Check It Out: Example Continued Find the distances between the points to the nearest tenth. d = (4 – (–4))² + (0 – 0)² d = (8)² + (0)² Simplify powers. d = 64 + 0 The distance between J and L is 8 units.
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Applying the Pythagorean Theorem and Its Converse 3-9 K and M Check It Out D. Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².
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Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Check It Out: Example D Continued Find the distances between the points to the nearest tenth. d = ((–4) – 0)² + (– 3 – (–3)² d = (–4)² + (0)² Simplify powers. d = 16 + 0 The distance between K and M is 4 units.
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Applying the Pythagorean Theorem and Its Converse 3-9 Problem of the Day The sum of the squares of two positive numbers is 100. One number is two more than the other. What are the numbers? 6 and 8
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Applying the Pythagorean Theorem and Its Converse 3-9 Example 3: Identifying a Right Triangle a 2 + b 2 = c 2 9 2 + 12 2 = 15 2 81 + 144 = 225 225 = 225 √ Substitute. Compare a² + b² to c². The side lengths form a right triangle. A. Tell whether the given side lengths form a right triangle. 9, 12, 15 Simplify. Add.
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Applying the Pythagorean Theorem and Its Converse 3-9 Example 3: Identifying a Right Triangle a 2 + b 2 = c 2 8 2 + 10 2 = 13 2 63 + 100 = 169 163 ≠ 169 x Substitute. Compare a² + b² to c². The side lengths do not form a right triangle. B. Tell whether the given side lengths form a right triangle. 8, 10, 13 Simplify. Add.
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Applying the Pythagorean Theorem and Its Converse 3-9 Check It Out a 2 + b 2 = c 2 5 2 + 6 2 = 9 2 25 + 36 = 81 61 ≠ 81 x Substitute. Compare a² + b² to c². The side lengths do not form a right triangle. C. Tell whether the given side lengths form a right triangle. 5, 6, 9 Simplify. Add.
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Applying the Pythagorean Theorem and Its Converse 3-9 Example 3B a 2 + b 2 = c 2 8 2 + 15 2 = 17 2 64 + 225 = 289 289 = 289 √ Substitute. Compare a² + b² to c². The side lengths form a right triangle. D. Tell whether the given side lengths form a right triangle. 8, 15, 17 Simplify. Add.
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Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz
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Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part I 1. width = 9 in., length = 40 in. 2. base length = 20 m, height = 15 m. 41 in. 25 m Find the length of the diagonal of the rectangle.
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Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part II 3. Q and R 4. S and T ≈ 6.3 ≈ 2.2 Find the distance between the points to the nearest tenth.
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Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part III 5. 12 cm, 13 cm, 16 cm 6. 11 ft, 60 ft, 61 ft no yes Tell whether the given side lengths form a right triangle.
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