# Diagonals in Geometry: Shapes & Formula

Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will learn the definition of a diagonal in geometry and see some examples in shapes. You will also learn the formula to determine how many diagonals are in a shape. Following the lesson is a brief quiz.

## What is a Diagonal in Geometry?

Before we get to the definition of a diagonal of geometry, we need to understand the components that make up the definition:

• A diagonal line, in informal terms, is simply a line that is at a slope.
• A line segment is a section of a line that has two defined endpoints.
• A polygon is a flat plane figure with at least three sides and angles. Usually, when we refer to a polygon, it has five or more sides and angles.
• A polyhedron is the three-dimensional counterpart of a polygon. It also usually has five or more sides. But the minimum is again three.
• Lastly, vertices are the points of a shape.

Now that we have all of that covered, a diagonal in geometry is a diagonal line segment that connects two nonconsecutive vertices of either a polygon or a polyhedron.

One more thing: based on the definition that a diagonal needs to connect two nonconsecutive vertices, it would be impossible to have a diagonal in a triangle or triangular pyramid.

## Images of Diagonals in Geometry

If you roll through one of these without stopping completely, you may get a ticket. That's right - a stop sign is an example of a polygon. In the image, you can see examples of diagonals in geometry in the stop sign.

A square is a polygon. A cube is what you call a three-dimensional square, which is a polyhedron. Informally, we would call this a box.

## Formula for Diagonals

If n is the number of sides of the polygon or polyhedron, then the formula to find the number of diagonals is:

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