1 / 14

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.

karleen
Download Presentation

Pythagorean Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related