wilsongeometry Mrs. Wilson
St. Pius X High School Geometry & Advanced Mathematics
http://stpiusxhs-kc.com
 
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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Last updated  2008/09/28 10:56:21 PDTHits  956