What is a Quadrilateral? - Definition, Properties, Types & Examples

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  • 0:05 Definitions and Examples
  • 2:38 Types of Properties…
  • 3:51 Lesson Summary
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Lesson Transcript
Instructor: Miriam Snare

Miriam has taught middle- and high-school math for over 10 years and has a master's degree in Curriculum and Instruction.

This lesson explains the definition and properties of a quadrilateral. We will look at examples of two categories of quadrilaterals. At the end, you will be able to test your knowledge with a quiz.

Definitions and Examples

A quadrilateral is a closed figure with four straight sides. You can make a quadrilateral by taking (or imagining) anything straight and thin you might have handy: pens, toothpicks, chopsticks, etc. A square is one type of a special quadrilateral.

Quadrilateral made of pencils

However, just to make it interesting, try to use four things that are not all the same length. Place your objects so that each end of one touches the end of another. I used pencils to form my quadrilateral, as you can see here. I placed each pencil tip so that it touches the eraser of another pencil. That way, I get a closed figure, meaning there are no gaps between sides and no side extends past the end of another side. Now we have our quadrilateral with four straight sides.

Let's simplify the figure by replacing the pencils with segments:

Quadrilateral PNCL

Each point where two sides touch is called a vertex. We name each vertex with a capital letter. Let's name our quadrilateral with the four vertices: P, N, C, and L. It also has four sides: the segments PN, NC, CL, and LP. To name the whole quadrilateral, we choose any vertex as a starting point and list all of the vertices going around either clockwise or counterclockwise. There are many possible names, including PNCL, LCNP, or CLPN.

If you play around a little with the objects that form your quadrilateral, it might be possible that you get a shape that looks something like this:

Concave quadrilateral made of pencils

This is still a quadrilateral because it follows the definition; it has four straight sides that form a closed figure. Again, we can simplify the figure with segments and name the vertices.

Concave quadrilateral

This quadrilateral has four vertices: A, R, O, and W. It has four sides: segments AR, RO, OW, and WA. The whole quadrilateral could be named AWOR, ROWA, or AROW.

The two quadrilaterals, PNCL and AROW, are examples of two different types of quadrilaterals. There are several other special quadrilaterals, such as parallelograms, trapezoids, and kites, but we won't get into the properties specific to each of those types in this lesson. We are only going to discuss two categories of quadrilaterals. Let's look at how to tell the difference between those two types in the next section.

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