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7.1 – Apply the Pythagorean Theorem

7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem:. If a triangle is a right triangle, then ( hypotenuse ) 2 = (leg) 2 + (leg) 2. c. leg. hypotenuse. a. leg. b. ( hypotenuse ) 2 = (leg) 2 + (leg) 2. c 2 = a 2 + b 2. 1. Find the value of x. c 2 = a 2 + b 2. H.

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7.1 – Apply the Pythagorean Theorem

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  1. 7.1 – Apply the Pythagorean Theorem

  2. Pythagorean Theorem: If a triangle is a right triangle, then (hypotenuse)2 = (leg)2 + (leg)2 c leg hypotenuse a leg b (hypotenuse)2 = (leg)2 + (leg)2 c2 = a2 + b2

  3. 1. Find the value of x. c2 = a2 + b2 H x2 = 152 + 362 x2 = 225 + 1296 x2 = 1521 x = 39

  4. 1. Find the value of x. c2 = a2 + b2 x2 = 42 + 92 H x2 = 16 + 81 x2 = 97

  5. 1. Find the value of x. c2 = a2 + b2 x2 = 62 + 32 x2 = 36 + 9 H x2 = 45

  6. 1. Find the value of x. c2 = a2 + b2 172 = x2 + 82 289 = x2 + 64 H 225 = x2

  7. 1. Find the value of x. c2 = a2 + b2 272 = x2 + 92 729 = x2 + 81 648 = x2 H

  8. 1. Find the value of x. c2 = a2 + b2 422 = x2 + 362 H 1764 = x2 + 1296 468 = x2

  9. 2. Find the area of the isosceles triangle. c2 = a2 + b2 H H 102 = h2 + 82 100 = h2 + 64 8 8 36 = h2 8 in2

  10. 2. Find the area of the isosceles triangle. c2 = a2 + b2 H 122 = h2 + 42 144 = h2 + 16 128 = h2 4 cm2

  11. 2. Find the area of the isosceles triangle. c2 = a2 + b2 H 442 = h2 + 242 1936 = h2 + 576 24 24 1360 = h2 24 m2

  12. 7.2 – Converse of the Pythagorean

  13. Pythagorean Theorem Converse: If c2 = a2 + b2, then the triangle is a right triangle c a b

  14. Acute Triangle: If c2 < a2 + b2, then the triangle is acute c a b

  15. Obtuse Triangle: If c2 > a2 + b2, then the triangle is obtuse c a b

  16. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 a. 8, 15, 17 172 = 82 + 152 8 + 15 > 17 289 = 64 + 225 8 + 17 > 15 289 = 289 15 + 17 > 8 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

  17. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! b. 3, 4, 9 3 + 4 > 9 7 > 9 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

  18. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 c. 10, 11, 14 142 = 102 + 112 10 + 11 > 14 196 = 100 + 121 10 + 14 > 11 196 221 < 11 + 14 > 10 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

  19. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 d. 61 = 25 + 36 5 + 6 > 7.8 61 = 61 5 + 7.8 > 6 6 + 7.8 > 5 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

  20. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 e. 144 = 13 + 100 3.6 + 10 > 12 > 144 113 3.6 + 12 > 10 10 + 12 > 3.6 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

  21. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c2 = a2 + b2 f. 4.3, 5.2, 6.1 4.3 + 5.2 > 6.1 37.21 = 18.49 + 27.04 4.3 + 6.1 > 5.2 < 37.21 45.53 5.2 + 6.1 > 4.3 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE

  22. HW Problem 7.1 #26 Ans: H H c2 = a2 + b2 c2 = a2 + b2 a x2 = 42 + 72 52 = a2 + 32 x2 = 16 + 49 25 = a2 + 9 x2 = 65 16 = a2 4 = a

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