# Similar Figures: Definition & Examples

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• 0:02 What Are Similar Figures?
• 0:56 Similar Polygons
• 2:15 Determining if…
• 3:37 Using Similar Figures
• 5:45 Lesson Summary
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Lesson Transcript
Instructor: Ryan Hultzman
Similar figures show up quite often in the world around us. In this lesson, we will discuss similar figures and their properties. At the end of the lesson, you can test your knowledge with a quiz.

## What Are Similar Figures?

To say that something is similar to something else is to say that the two things share common characteristics. For example, you and I may be brainstorming on how to solve a particular problem, and you tell me the approach you would take. I then tell you that your approach is similar to the plan I was thinking of. This means that our ideas on how to solve the problem are much the same but could have small differences as well.

In mathematics, saying that two figures are similar means that they share a common shape. They can be different sizes, but they must have the same shape. For example, observe this image of the butterflies:

The butterflies have the same shape but are different sizes. Therefore, the butterflies are similar.

## Similar Polygons

A polygon is a 2-dimensional object with a minimum of three straight sides and three angles. Some common polygons that we are familiar with are triangles, rectangles, hexagons, and octagons. Two polygons can be similar. For example, consider these two similar rectangles:

As we've discussed, similar figures have the same shape. Therefore, when we have two similar figures, one is a larger or smaller version of the other. Because of this, when two polygons are similar, their sides are proportional. Being proportional means the ratios of corresponding sides on similar polygons are all equal. For example, consider these two similar rectangles. Notice that the ratio of the corresponding shorter sides is equal to the ratio of the corresponding longer sides.

Ratio of shorter sides = 2/6 = 1/3
Ratio of longer sides = 3/9 = 1/3

Since 1/3 = 1/3, these two rectangles are proportional.

## Determining if Two Polygons Are Similar

We can use the fact that the sides of similar polygons are proportional to determine if two polygons are similar. To determine if two polygons are similar, we simply set up the ratios of corresponding sides and see if they are equal. If so, then the two polygons are similar. If not, then they are not similar.

For example, consider this image. Are the two polygons similar?

To decide if these two polygons are similar, we look at the ratios of the corresponding sides. The polygon has four sides, so we will look at the ratio of each of the corresponding sides. If all of them are equal, then the polygons are similar:

• Side 1: 4/8 = 1/2
• Side 2: 1/2
• Side 3: 5/10 = 1/2
• Side 4: 6/12 = 1/2

We see that the ratios of corresponding sides are equal. Therefore, the sides are proportional, and the two polygons are similar.

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