# Concave & Convex Polygons: Definition & Examples

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• 0:00 Polygon Classification
• 0:25 Convex Polygons
• 0:40 Concave Polygons
• 1:20 Mathematical…
• 2:20 Real Life Applications…
• 3:05 Lesson Summary
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Lesson Transcript
Instructor: Elizabeth Often

Elizabeth has taught high school math for over 10 years, and has a master's in secondary math education.

In this lesson, we'll explore one of the main ways of classifying polygons - as convex or concave. We'll also learn how you can determine if a polygon is convex or concave.

## Polygon Classification

I remember taking my driving test and having to memorize all the different shapes of the road signs - rectangles, triangles, octagons. I wondered if there was a way to classify all of these different shapes. In this lesson, we'll explore two classes of polygons - convex and concave - and discuss some easy ways of telling them apart. It's important to know that every polygon can be classified as convex or concave.

## Convex Polygons

In a convex polygon, no diagonal goes outside the figure as it travels from one corner to the other. Another property of convex polygons is that no angle inside the polygon will have a measure greater than 180 degrees.

## Concave Polygons

In a concave polygon, at least one diagonal passes outside the figure.

In addition, at least one angle inside the polygon will have a measure greater than 180 degrees. In the polygon, here, the red diagonals pass outside the figure as they travel from one corner to the other, and one of the blue angles is larger than 180 degrees.

You can use the word cave to help you remember the difference between convex and concave polygons. A convex polygon has all its vertices, or corners, pointing out from the center, but a concave polygon looks like it has been caved in.

## Mathematical Applications of Polygons

Convex polygons are used very frequently in basic geometry. Many of the basic polygons that you learn about in a geometry course, including the square, the rectangle and the parallelogram, are convex. Additionally, some of the formulas that you will learn in geometry, such as the angle sum theorem, only work for convex polygons.

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