Geometry unit 8, sec 8.1+8.2
Ratio and Proportion
Guided notes:
I) Vocabulary:
A) Ratio: A comparison of same quantities (or units), usually expressed in fractional form.
Ex. a/b a:b or you can use "a to b" where b is not = 0.
B) Proportion: Two ratios set equal to each other
1. Means: bottom left, top right, or 2 inside terms.
2. Extremes: top left, bottom right, or 2 outside terms.
3. The means and the extremes can be multiplied and the results are still the same.
4. Cross products are equal!
In a proportion, the product of the means is equal to the product of the extremes.
Example:
a/b = c/d
ad = bc
1) 1/2 = 2/4
(1)(4) = (2)(2)
4 = 4
2) 9/12 = 3/4
(9)(4) = (12)(3)
36 = 36
Geometric Mean: If two means are equal, then they are the geometric mean, or the mean proportional.
For 2 positive numbers “a” and “b” the positive number x, such that
a/x = x/b
ab = x(x)
ab = x2
1) what is the geometric mean of 3 and 9?
3/x = x/9
27 = x2
x = the square root of 27
2) what is the geometric means of 9 and 4?
9/x = x/4
36 = x2
x = 6
