Geometry/Chapter 5/Lesson 2

Introduction

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We will be reviewing proportions, the properties of proportions, and how to solve them.

Proportions

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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.

1 Are   =   a proportion?

Yes
No

2 Are   =   a proportion?

Yes
No

Solving with x

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How do we solve porpotions with   or any variable?

Problem #1

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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:   =