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- 1. a b c 222 cba
- 2. This is a right triangle:
- 3. We call it a right triangle because it contains a right angle.
- 4. The measure of a right angle is 90o 90o
- 5. The little square 90o in the angle tells you it is a right angle.
- 6. About 2,500 years ago, a Greek mathematician named Pythagorus discovered a special relationship between the sides of right triangles.
- 7. Pythagorus realized that if you have a right triangle, 3 4 5
- 8. and you square the lengths of the two sides that make up the right angle, 2 42 3 3 4 5
- 9. and add them together, 3 4 5 2 42 3 22 43
- 10. 22 43 you get the same number you would get by squaring the other side. 222 543 3 4 5
- 11. Is that correct? 222 543 ? 25169 ?
- 12. It is. And it is true for any right triangle. 8 6 10222 1086 1006436
- 13. The two sides which come together in a right angle are called
- 14. The two sides which come together in a right angle are called
- 15. The two sides which come together in a right angle are called
- 16. The lengths of the legs are usually called a and b. a b
- 17. The side across from the right angle a b is called the
- 18. And the length of the hypotenuse is usually labeled c. a b c
- 19. The relationship Pythagorus discovered is now called The Pythagorean Theorem: a b c
- 20. The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c, a b c
- 21. then a b c .222 cba
- 22. You can use The Pythagorean Theorem to solve many kinds of problems. Suppose you drive directly west for 48 miles, 48
- 23. Then turn south and drive for 36 miles. 48 36
- 24. How far are you from where you started? 48 36 ?
- 25. 482 Using The Pythagorean Theorem, 48 36 c 362 + = c2
- 26. Why?Can you see that we have a right triangle? 48 36 c 482 362 + = c2
- 27. Which side is the hypotenuse?Which sides are the legs? 48 36 c 482 362 + = c2
- 28. 22 3648 Then all we need to do is calculate: 12962304 3600 2 c
- 29. And you end up 60 miles from where you started. 48 36 60 So, since c2 is 3600, c is 60.So, since c2 is 3600, c is
- 30. Find the length of a diagonal of the rectangle: 15" 8" ?
- 31. Find the length of a diagonal of the rectangle: 15" 8" ? b = 8 a = 15 c
- 32. 222 cba 222 815 c 2 64225 c 2892 c 17c b = 8 a = 15 c
- 33. Find the length of a diagonal of the rectangle: 15" 8"17
- 34. Practice using The Pythagorean Theorem to solve these right triangles:
- 35. 5 12 c = 13
- 36. 10 b 26
- 37. 10 b 26 = 24 (a) (c) 222 cba 222 2610 b 676100 2 b 1006762 b 5762 b 24b
- 38. 12 b 15 = 9

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