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10.5 – The Pythagorean Theorem

10.5 – The Pythagorean Theorem. leg leg. hypotenuse leg leg. hypotenuse leg leg

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10.5 – The Pythagorean Theorem

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  1. 10.5 – The Pythagorean Theorem

  2. leg leg

  3. hypotenuse leg leg

  4. hypotenuse leg leg Pythagorean Theorem: For a right triangle with legs a and b and hypotenuse c, then a2 + b2 = c2, where a is the smaller of the two legs.

  5. Ex. 1 Find the length of the missing side. a 25 10

  6. Ex. 1 Find the length of the missing side. a 25 10 a2 + b2 = c2

  7. Ex. 1 Find the length of the missing side. a 25 10 a2 + b2 = c2 a2 + (10)2 = (25)2

  8. Ex. 1 Find the length of the missing side. a 25 10 a2 + b2 = c2 a2 + (10)2 = (25)2 a2 + 100 = 625

  9. Ex. 1 Find the length of the missing side. a 25 10 a2 + b2 = c2 a2 + (10)2 = (25)2 a2 + 100 = 625 a2 = 525

  10. Ex. 1 Find the length of the missing side. a 25 10 a2 + b2 = c2 a2 + (10)2 = (25)2 a2 + 100 = 625 a2 = 525 a ≈ 22.91

  11. Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29

  12. Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs.

  13. Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a2 + b2 = c2

  14. Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a2 + b2 = c2 (20)2 + (21)2 = (29)2

  15. Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a2 + b2 = c2 (20)2 + (21)2 = (29)2 400 + 441 = 841

  16. Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a2 + b2 = c2 (20)2 + (21)2 = (29)2 400 + 441 = 841 841 = 841

  17. Ex. 2 Determine whether the following side measures form right triangles. a. 20, 21, 29 Shorter lengths must be the legs. So, a2 + b2 = c2 (20)2 + (21)2 = (29)2 400 + 441 = 841 841 = 841 , so they form a rt. triangle!

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