# Geometry/Chapter 5/Lesson 2

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## 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: =