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Pythagorean Theorem

Pythagorean Theorem. a 2 + b 2 = c 2. Parts of a Right Triangle. Hypotenuse. c. (Longest Side). Leg. [Opposite the 90 ° angle]. a. Leg. b. Example 1 Is the triangle below a right triangle?. a 2 + b 2 = c 2. 4 2 + 3 2 = 5 2. 5. 16 + 9 = 25. 4. 25 = 25. YES. 3.

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Pythagorean Theorem

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  1. Pythagorean Theorem a2 + b2 = c2

  2. Parts of a Right Triangle Hypotenuse c (Longest Side) Leg [Opposite the 90° angle] a Leg b

  3. Example 1 Is the triangle below a right triangle? a2 + b2 = c2 42 + 32 = 52 5 16 + 9 = 25 4 25 = 25 YES 3

  4. Example 2 Is the triangle below a right triangle? a2 + b2 = c2 52 + 122 = 142 25 + 144 = 196 14 ? 5 169 = 196 NO 12

  5. YOUR TURN Is the triangle below a right triangle? a2 + b2 = c2 92 + 122 = 152 81 + 144 = 225 15 ? 9 225 = 225 YES 12

  6. Example 3 Find the missing side length a2 + b2 = c2 13 a2 + 122 = 132 a a2 + 144 = 169 -144 =-144 a2 = 25 √ √ 12 a = 5

  7. Find the missing side length a2 + b2 = c2 30 ft a 24 ft

  8. Workbook Pg. 7 -- #2 Find the missing side length 24 in a2 + b2 = c2 102 + 242 = c2 10 in c 100 + 576 = c2 676 = c2 √ √ 26 = c

  9. Workbook Pg. 7 -- #3 Find the missing side length a2 + b2 = c2 17 cm 82 + b2 = 172 8 cm 64 + b2 = 289 -64 = -64 b2 = 225 √ √ b b = 15

  10. Workbook Pg. 7 -- #4 Find the missing side length a2 + b2 = c2 82 + 52 = x2 64 + 25 = x2 x 89 = x2 √ √ 8 m 9.433981132 = x 9.4 = x Round to the nearest tenth 5 m

  11. Workbook Pg. 7 -- #5 Find the missing side length x a2 + b2 = c2 6.2 cm x2 + 6.22 = 7.52 x2 + 38.44 = 56.25 -38.44 -38.44 7.5 cm x2 = 17.81 √ √ x = 4.220189569 x = 4.2 Round to the nearest tenth

  12. Workbook Pg. 7 -- #6 Find the missing side length a2 + b2 = c2 x 8 in x2 + 82 = 152 x2 + 64 = 225 -64 -64 15 in x2 = 161 √ √ x = 12.68857754 x = 12.7 Round to the nearest tenth

  13. Workbook Pg. 7 -- #7 A ladder leans against a wall 6 ft above the ground. The base of the ladder is 3 ft from the wall. How long is the ladder? a2 + b2 = c2 W A L L 62 + 32 = x2 6 ft Ladder x 6 ft 36 + 9 = x2 45 = x2 √ √ 6.708203932 = x Round to the nearest tenth 6.7 = x ground 3 ft

  14. Workbook Pg. 7 -- #8 A small rectangular tray measures 16 cm by 18 cm. How long is the diagonal? a2 + b2 = c2 182 + 162 = x2 324 + 256 = x2 x 16 cm 580 = x2 √ √ TRAY 24.08318916 = x Round to the nearest tenth 18 cm 24.1 = x

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