wilsongeometry Mrs. Wilson St. Pius X High School Geometry & Advanced Mathematics http://stpiusxhs-kc.com Send e-mail Chapter 7-Similarity 7.1 Ratio-given 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 means-extremes property.    7.2  1.  means-extremes 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.  265-266/ 1-26 omit 10 1/22-1/23   7.2 pg.  269-270/ 1-22             square root problems 1-20
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