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Warm Up

Warm Up. Use the figure for problems 1 and 2. round to the nearest hundredth. 1) Find the height a of the triangle. c. 10. 8. a. 6. 9. 2) Find the length of side c. c = 8 2 + 9 2. c = 64 + 81. c = 145. Warm Up. B. Find the distances between the points C and D

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Warm Up

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  1. Warm Up Use the figure for problems 1 and 2. round to the nearest hundredth 1) Find the height a of the triangle c 10 8 a 6 9 2) Find the length of side c c = 82 + 92 c = 64 + 81 c = 145

  2. Warm Up B Find the distances between the points C and D E and F A and B C 5 units A 6 units ??? F E D

  3. Lesson3-9 The Pythagorean Thm and its Converse You'll Learn how to Use the Distance formula and the converse of PYTH.THM

  4. 1 EXAMPLE Use the converse of Pythagorean Theorem The converse of the Pythagorean Theorem If any positive numbers, a,b, and c satisfy the Pythagorean theorem a2 + b2 = c2 then a, b and c form a right triangle Tell whether the given sides lengths form a right triangle. i) 8, 15, 17 ii) 8, 10, 13 Checking (c is the longest side) Checking (c is the longest side) a2+ b2= c2 a2+ b2= c2 82 + 152 172 = 82 + 102 132 = 289 = 169 64 + 225 = 64 + 100 289 289 = 164 169 = They form a right triangle They DO NOT form a right triangle

  5. 1 EXAMPLE Use the Distance Formula Find the distance between the points. Method1: Using Pythagorean Theorem B 5 (4, 4) c = 32 + 52 x2, y2 3 c c = 9 + 25 A (-1, 1) c = 34 x1, y1 Method2: Using Distance Formula 4 1 4 -1 5 3 25 9 34

  6. 2 EXAMPLE Find the distance between the points Using Distance Formula -3 0 0 -4 4 -3 (-4, 0) x1, y1 16 9 25 (0, -3) x2, y2

  7. Lesson Quiz: Part I Find the length of the diagonal of the rectangle. 1. width = 9 in., length = 40 in. 2. base length = 20 m, height = 15 m.

  8. Lesson Quiz: Part II Find the distance between the points to the nearest tenth. 3.Q and R 4.S and T

  9. Lesson Quiz: Part III Tell whether the given side lengths form a right triangle. 5. 12 cm, 13 cm, 16 cm no 6. 11 ft, 60 ft, 61 ft yes

  10. Lesson Quiz for Student Response Systems 1. Find the length of the diagonal of the rectangle. width = 5 m, length = 12 m A. 8 m B. 11 mC.13 m D.17 m

  11. Lesson Quiz for Student Response Systems 2. Find the distance between the points to the nearest tenth. Q and S A. 6.0 m B. 6.1 mC.7.0 m D.37.1 m

  12. Lesson Quiz for Student Response Systems 3. Tell whether the given side lengths form a right triangle. 12 ft, 13 ft, 14 ft A. yes B. no

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