Geometry/Chapter 5/Lesson 2
|This page is under construction. Content is likely to be revised significantly in the near future.|
Introduction[edit | edit source]
We will be reviewing proportions, the properties of proportions, and how to solve them.
Proportions[edit | edit source]
A proportion is a statement that states that two ratios are equal.
- EXAMPLE: and are equal, and thus are a proportion: = .
An extended proportion is similar to an extended ration from the last lesson: A statement that states that three or more rations are equal.
- EXAMPLE: = =
All proportions have 4 parts known as the extremes and means. In = , the extremes are and , while the means are and . The Cross-Product Property states that the products of the extremes and means are equal. So:
- • =
- • =
You can use the cross-product property to check if two ratios are a proportion.
Solving with [edit | edit source]
How do we solve porpotions with or any variable?
Problem #1[edit | edit source]
- Solve the proportion
Solving for , you would multiply the extremes ( and ) and the means ( and ):
And simply work out the problem from there:
So, alas, the in = is ... So: =