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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