Geometry/Chapter 5/Lesson 2

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Introduction[edit]

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

Proportions[edit]

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 [edit]

How do we solve porpotions with or any variable?

Problem #1[edit]

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: =