Chapter 7Similarity 7.1 Ratiogiven any two numbers, x and y, a ratio is x divided by y. A ratio can be written in three ways 1. x to y 2. x:y 3. x/y (written as a fraction) A ratio always needs to be simplified. The process is the same as simplifying a fraction. Ex. 20 to 16, both numbers can be divided by 4 so the simplified expression is 5 to 4 Whenever there is a ratio in a “word problem” set the problem up like this: Ex. The ratio of two complementary angles is 2:3. We know that complementary angles add up to 90. Let one angle be 2x and the other angle 3x. The equation would be 2x + 3x = 90. Solve for x and plug the number into 2x and 3x. 2x + 3x = 90 5x = 90 x = 18 2x = 2(18) = 36 3x = 3(18) = 54 When solving proportions (two ratios that are equal to each other), cross multiply. Cross multiplying is called the meansextremes property. 7.2 1. meansextremes property: a/b = c/d is equivalent to ad = bc, (cross multiplying) 2. the means and extremes can be interchanged 3. the reciprocals of each ratio are equal Simplifying radicals A radical is a number with a square root sign. To simplify a radical, the largest perfect square factor needs to be found. Ex. Factors of 12 are 1,12 2,6 3,4 Perfect squares 1² = 1 x 1 = 1 2²= 2 x 2 =4 3² = 9 4² = 16 5² = 25 6² = 36 7² = 49 8² = 64 9² = 81 10² = 100 11² = 121 12² = 144 ex. Simplify square root (I cannot put in the square root symbol, from now on “sr” will be square root) of 12: we will pick factors 3,4 from above because 4 is a perfect square, sr 12 = sr 4 x sr 3 (sr 4 = 2, sr 3 cannot be simplified) sr 12 = 2 sr 3 I know this is confusing on the computer. I can’t use symbols. Geometric mean the geometric mean between any two numbers p and q is: p/x = x/q Ex. Find geometric mean between 4 and 9 4/x = x/9 cross multiply 4(9) = x(x) 36 = x² 6 = x Homework 1/22 7.1 pg. 265266/ 126 omit 10 1/221/23 7.2 pg. 269270/ 122 square root problems 120

