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10-1: Ratio, Proportion, and Similarity

Proportion: 2 ratios equal to eachother.

a:b=c:d "a is to b as c is to d."

Extended Proportion: 1/3=3/9=15/45; more than 2 ratios(3 or more). Reduced fraction= Similarity Ratio.

Properties of Proportion: a/b=c/d (USE!!!)

1. means-extremes property

cross-product

cross multiply(ad=bc)ad are the extremes, bc are the means.

2. b/a=d/c

3. a/c=b/d

4. a+b/b=c+d/d

Are the polygons similar? If so, write a similarity ratio.

(~) Similar: Angles are congruent, sides are proprtional.

Example: 10:5=12:6=14:7

10/5=12/6=15/7

2=2=2.

therefore, yes, the polygons would be similar.

Problem 10-1

If x/y=5/8, is the following true or false?

8x=5y (true)