Ratios and Proportions
A ratio is a comparison of two quantities by division. A ratio can be written as number 1/2, 1:2, or 1 to 2. An extended ratio compares more than two numbers. If two ratios are equivalent, you can write them as a proportion. A proportion would be written like 3:6 = 9:18. The first and last numbers in a proportion are the extremes, and the middle two are the means. That would mean that 3 and 18 are the extremes, and 6 and 9 are the means. You can also write an extended proportion. An extended proportion would be written like 2:6 = 1:3 = 6:18
Similar figures are the same shapes but not the same size. Proportions and ratios can be used to determine if shapes are similar, and to find missing side lengths. A scale factor is the ratio of the corresponding measurements of two similar figures.
Proving Similar Triangles
Similar triangles can be proven by using either the SSS, SAS, or AA theorems. These are used by determining if all three sides are proportional, two sides and the angle they make are proportional, or if two angles are proportional between two or more triangles.