## Friday, December 22, 2006

### Geometry 8.1+8.2 Ratio and Proportion

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

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