Copyright

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.

Note that each of the three diagonals are connected by nonconsecutive vertices of the stop sign.
Some diagonals in a hexagon

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.

Here is a cube with two diagonals indicated in blue and red, connected by nonconsecutive vertices
Some diagonals in a cube

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:

n (n-3)/2

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account
Support