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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Learn how you can use proportions to find missing sides and how to increase or decrease the sizes of objects to create models of them in this video lesson.

Things are in **proportion** if the ratios are equal to each other. For example, if I compared the measurements of a model car to its life-size counterpart, I would find that all those ratios are equal to each other. Measuring the wheel of a model toy car, I find that it measures 1.5 inches. Its life size counterpart has a wheel that measures 18 inches. My wheel ratio is 1.5/18 or 1.5:18.

If the model car is 1/12 life size, is the wheel in proportion? I check by dividing both ratios:

1.5/18 = 0.0833

1/12 = 0.0833

Do I get the same answer for both? I do, so they are proportional.

To keep things in proportion when increasing or decreasing their sizes, all I have to do is to make sure to multiply all the numbers in my original ratio by the same amount.

Here's an example. To make dog cookies, I use a ratio of 1 cup oatmeal to 1 cup peanut butter. That gives me a ratio of 1:1. If I wanted to double the amount of cookies I make without changing the recipe to keep things in proportion, I would simply multiply my ratio by 2 to get 2:2. That means I would need to use 2 cups oatmeal and 2 cups peanut butter to make double the amount of cookies.

You can check to see if you did the math right by dividing your ratios to see if they are proportional. If the ratios divide into the same number, then they are proportional.

For example, the ratios 4:5 and 8:10 are proportional because both divide into the same number:

4/5 = 0.8

8/10 = 0.8

On the other hand, the ratios 8:10 and 7:10 are not proportional because they don't divide into the same number:

8/10 = 0.8

7/10 = 0.7

If you know that two ratios are proportional, you can actually use this information to find the length of a missing side.

For example, say you have a model of the house you are in, and you want to find out how tall your house is. You know how long the room you are in is as well as how long that same room is in the model. You can easily measure how tall the model house is but you can't easily measure how tall your life-size house is. So, how do you use proportions to help you? Let's see how this works.

You know that your model house is proportionate to your life-size house, so all the ratios have to be equal. The length of the room you are in is 12 feet in real life and 1 foot in the model house. This gives you a ratio of 12:1 for the length of the room. The model house measures 2 feet tall. You don't know the life-size height of the house, so you label that as *x*. Your house height ratio is *x*:2.

I've written my ratios as real life:model, so I make sure to keep all my ratios like that. These two ratios must be equal to each other so I write:

12:1 = *x*:2

I know I can also rewrite my ratios as fractions:

12/1 = *x*/2

Now I can use algebra to help solve for *x*. I know to get *x* by itself I need to multiply by 2 on both sides. I do that, and I get an answer of 24. So, that means my house is 24 feet tall. I have found my missing side!

What have we learned? We've learned that being in **proportion** means that the ratios are equal to each other. To keep things in proportion when increasing or decreasing size, we make sure to multiply all our numbers in our ratio by the same amount. To check whether things are in proportion, we check to see if the ratios divide into the same number. And, we can use proportions to find missing sides by setting the two ratios equal to each other and finding the missing side.

After reviewing this lesson, you should be able to:

- Define proportion
- Explain how to keep things in proportion when you want to increase or decrease a size
- Describe how to find a missing item that is in proportion to another item

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Geometry: High School15 chapters | 160 lessons

- Ratios and Proportions: Definition and Examples 5:17
- Geometric Mean: Definition and Formula 5:15
- Angle Bisector Theorem: Definition and Example 4:58
- Solving Problems Involving Proportions: Definition and Examples 5:22
- The Transitive Property of Similar Triangles 4:50
- Triangle Proportionality Theorem 4:53
- Constructing Similar Polygons 4:59
- Properties of Right Triangles: Theorems & Proofs 5:58
- The Pythagorean Theorem: Practice and Application 7:33
- The Pythagorean Theorem: Converse and Special Cases 5:02
- Similar Triangles & the AA Criterion 5:07
- What is a Polygon? - Definition, Shapes & Angles 6:08
- Go to High School Geometry: Similar Polygons

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