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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. A C B N

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. A C B N ANCN BN =

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. A C B N ABAC AN =

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. A C B N ABAC AN = ABBC BN = 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

A C B N 63 x y w z = 9 w = 9

A C B K x 9 y z w 15

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

8 in Find Area

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. a c b B A C

< 12 Neither +<+>+= ObtuseAcuteRight 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

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)

Lots of examples

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

A B C

Find x Hypotenuse Look at what they want and what they give you, then use the correct trig ratio. Opposite opposite, hypotenuse USE SIN! x 20 Pg 845 Anglesincostan 34 o Or use the calculator

Find y Hypotenuse Look at what they want and what they give you, then use the correct trig ratio. Adjacent adjacent, hypotenuse USE COS! y 20 Pg 845 Anglesincostan 34 o Or use the calculator

Find x Look at what they want and what they give you, then use the correct trig ratio. Adjacent Opposite Adjacent, Opposite, use TANGENT! 30 4 Pg 845 Angle sin cos tan 81 o o o If you use the calculator, you would put tan -1 (7.5) and it will give you an angle back.

Word Problems Hills, Buildings, Trees

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14-23 Geo mean legs, alt, pythag Pythag area of triangle , State trig ratios Trig word prob VECTORS!!