Aliens and Trapezoids

I am always looking for ways to help my students remember things.  For example, when we learn about the properties of one, I sing (yes I do, and a little off key) One is the Loneliest Number.  Since there are so many quadrilaterals to learn (*7 in all), I create quadrilateral stories.  Here is one of my students' favorites.  (Keep in mind, these are college students.)

Once upon a time, I planted a broccoli garden in my backyard.  Since I love geometry, I placed triangle statues all around my garden.  Every morning I would go out to my garden to weed, hoe, fertilize, and water my precious broccoli plants.  One morning, I noticed several of my plants had been eaten.  I was one upset lady; so, I decided to stay up all night and watch to see which critters had the nerve to venture into my garden for a broccoli feast.

That night, I sat at my bedroom window watching the garden.  All of a sudden, out of the sky, came a UFO which landed in my backyard.  As I watched, the door of the UFO opened (I use my arms to imitate the opening door while I say, S-q-e-a-k!) and out came some little aliens.  As they approached my broccoli, they repeated, "Zoid, zoid, zoid".  (I use a high alien like voice.) Sure enough, they ate several of my plants!  They then proceeded back to their spaceship and flew away. 

The same thing happened the following night and the night after that; so, I knew something had to be done.  I went to my garage, and got out my trusty chain saw to cut off the top of each of my triangles.  (I imitate the noise of a chain saw.)  Inside each cut off triangle I placed a bunch of broccoli to entice my visitors.  I knew if those aliens got inside, they would never get out because of the slanting sides.  I went back into my house to wait.

Sure enough, like clockwork, the UFO returned.  Again, the door of the UFO opened (s-q-e-a-k!) and out came the same little aliens. They proceeded to my cut off triangles, and perched on the edge peering down at the broccoli, all the while saying, "Zoid, zoid, zoid".  One by one they leaped inside to eat the broccoli, and guess what.  I trapped-a-zoid!  Okay, you may not be laughing, but I swear this story does help my students to remember what a trapezoid is. 

Let's discuss a couple of important math things about trapezoids that you may not be aware of.   In my story, the trapezoid is an isosceles trapezoid or as sometimes called, a regular trapezoid.  Not only does it have one set of opposite sides parallel, but it also has one set of opposite sides equal (marked with the black line segments).  It also has one line of symmetry which cuts the trapezoid in half (the blue dotted line).  This special trapezoid is usually the one taught by most teachers, but it is really a special kind of trapezoid. 

   trapezoid                                   isosceles trapezoid

For a quadrilateral to be classified as a trapezoid, the shape only needs to have one set of opposite sides parallel as seen in figure one.  The first trapezoid is the one that sometimes appears on tests to "trick" our students.

In the second figure (the isosceles or regular trapezoid), the sides that are not parallel are equal in length and both angles coming from a parallel side are equal (shown on the right).  Lucky for me that I used the second trapezoid for my trap or my zoids would have been long gone, and with my entire crop of broccoli, too!

*square, rectangle, rhombus, parallelogram, trapezoid, kite, trapezium