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Pg 586-587: 1 - 21 all; Pg 582-584: 1 - 24 all

Pg 586-587: 1 - 21 all; Pg 582-584: 1 - 24 all. Chapter 9 Review. Theorem 9.1: If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. C. B. A. N.

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Pg 586-587: 1 - 21 all; Pg 582-584: 1 - 24 all

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  1. Pg 586-587: 1 - 21 all; Pg 582-584: 1 - 24 all

  2. Chapter 9 Review

  3. Theorem 9.1: If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. C B A N

  4. Theorem 9.2 (Geo mean altitude): When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse. C AN CN = CN BN B A N

  5. Theorem 9.3 (Geo mean legs): When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg. C AB AC = AC AN B A N

  6. Theorem 9.3 (Geo mean legs): When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg. One way to help remember is thinking of it as a car and you draw the wheels. Another way is hypotenuse to hypotenuse, leg to leg C AB AB AC BC = = AC BC AN BN B A N

  7. C B A N y z x 6 3 w 6 + 3 = 9 w = 9

  8. C w x A 9 K z y 15 B

  9. The Pythagorean Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. a b c

  10. Find Area 8 in

  11. Converse of Pythagorean Theorem: If the square of the hypotenuse is equal to the sum of the squares of the legs, then the triangle is a right triangle. C a b B A c

  12. 121 64 36 64 81 3 1 4 5 + 6 < 12 Neither 16 + < + > + = Obtuse Acute Right Watch out, if the sides are not in order, or are on a picture, c is ALWAYS the longest side and should be by itself

  13. Remember, small side with small angle. Common Sense: Small to big, you multiply (make bigger) Big to small, you divide (make smaller) For 30 – 60 – 90, find the smallest side first (Draw arrow to locate)

  14. Lots of examples

  15. These are trig ratios that describe the ratio between the side lengths given an angle. sine  sin cosine  cos Tangent  tan A device that helps is: SOHCAHTOA B in ppyp os dj yp an ppdj HYPOTENUSE OPPOSITE A C ADJACENT

  16. B C A

  17. Hypotenuse Opposite Find x opposite, hypotenuse USE SIN! x 20 Pg 845 Angle sin cos tan 34o .5592 .8290 .6745 Or use the calculator Look at what they want and what they give you, then use the correct trig ratio.

  18. Hypotenuse Adjacent Find y adjacent, hypotenuse USE COS! y 20 Pg 845 Angle sin cos tan 34o .5592 .8290 .6745 Or use the calculator Look at what they want and what they give you, then use the correct trig ratio.

  19. Opposite Adjacent Find x Adjacent, Opposite, use TANGENT! 30 4 Pg 845 Angle sin cos tan 81o .9877 .1564 6.3138 82o .9903 .1392 7.1154 83o .9925 .1219 8.1443 If you use the calculator, you would put tan-1(7.5) and it will give you an angle back. Look at what they want and what they give you, then use the correct trig ratio.

  20. Word Problems • Hills, Buildings, Trees

  21. Pg 586-587: 1 - 21 all; Pg 582-584: 1 - 24 all

  22. 14-23 • Geo mean legs, alt, pythag • Pythag area of triangle • 45-45-90, 30-60-90 • State trig ratios • Trig word prob • VECTORS!!

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