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.
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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:
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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:
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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.
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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.
Types and Properties of Quadrilaterals
Depending on how the sides of a quadrilateral are connected to one another, quadrilaterals can be divided into two categories: convex and concave. To tell the difference between a convex and a concave quadrilateral, draw (or imagine) segments between each pair of unconnected vertices. If both segments lie inside the quadrilateral, then the figure is convex. If one of the segments lies outside of the quadrilateral, then the figure is concave.
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