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GEOMETRY/TRIGONOMETRY 2 Name _______________________ Ratios: the quotient of two numbers, a b, usually written a b or a:b, b 0. simplest form: each term of the ratio is reduced by their _____________________. Ratios can be used to compare numbers, such as lengths or angle measures, but the quantities being compared must be in the same __________. Ratios have no units. Ratios can be used to compare three or more numbers, i.e., a:b:c. Proportions: a b an equation that states that two ratios are _______________. c d a:b = c:d _______________: the first and last terms of a proportion _______________: the middle terms of a proportion Properties of Proportions (“a prop. of prop.”) means-extremes property: the _______________ of the means is equal to the _______________ of the extremes. If interchange the means: If reciprocal of the ratios: If add 1 to both sides: If 2 3 2 3 2 3 2 3 4 6 4 6 4 6 4 6 , then _____ = _____ , then _____ = _____ , then _____ = _____ , then _____ = _____ Express each ratio in simplest form. 1) AB:AC ________ 2) mB mA 3) the measure of the largest angle to the smallest angle A ________ 12 91° 24 ________ B 26° 27 C Express the ratio AB: AD in simplest form. (4) (5) (6) AB 12 cm 1m 25 cm AD 15 cm 0.3 m 2m AB:AD : : : In exercises 7-9, find the measure of each angle. 7) Two complementary angles have measures in the ratio 2:3 7) __________ 8) The measures of the angles of a triangle are in the ratio 2:2:5. 8) __________ 9) The ratio of the measures of the exterior angles of a pentagon is 2:3:4:4:5. Find the measure of the largest interior angle. 9) __________ Complete and name the property of proportions you used. 10) If 12) If x 5 8 y 3 , then 2x = _____ 2 11) If y 3 , then = _____ x 8 13) If 14) If 4:x = y:8, then 8:x = _____ a) 4 7 21 b) a7 7 7 7 x x7 y , then = _____ 8 7 3 4 , then 3x = _____ 15) If 4:x = y:8, then xy = _____ 16) Which proportions are equivalent to a x 25 21 a 7 4 ? 21 c) 7 a 21 4 d) 21 a 7 4 Use the means-extreme property to find the value of x. 17) 20) 6 x x-5 2 3 5 18) 5 6 In the figure 21) AD DC AB . BC AD DC 23) 4 6 24) 8 25) 18 20 x-2 x 1 9 2x x2 19) 1 4 12 x -1 22) x3 1 2 3 5 Complete the table. AC AB B BC 8 13 16 18 15 24 A D C