Watch this video lesson to learn what a trapezoid has to do with a triangle. Also, learn the special words that describe the various parts of a trapezoid. You will also see special types of trapezoids.
A trapezoid is a four-sided flat shape with one pair of opposite parallel sides. It looks like a triangle that had its top sliced off parallel to the bottom. Usually, the trapezoid will be sitting with the longest side down, and you will have two sloping sides for the edges. The top side is usually shorter than the bottom side. Doesn't it look like a triangle that had its top cut off?
Examples of trapezoids
Try picturing all kinds of triangles and then cutting off their tops. You will be left with a bunch of trapezoids.
Trapezoids have one property that must be obeyed. The property is that it must have one pair of parallel sides. If you are looking at a trapezoid, you will see that it has two flat sides. These flat sides are the sides that are parallel to each other. If you extended these lines, they would never meet. Try it.
When working with trapezoids, there are a few words that we must add to our vocabulary.
The first word is bases, which are the sides that are parallel to each other. Picture a triangle and the bottom side will be one of your bases. The side that is created by slicing off the top of the triangle is the other base.
The second word to consider is legs. These are the sloping sides that form the left and right edge of a trapezoid that is sitting with the longest side down. Going back to the sliced triangle, the legs are the sides that go up and meet at the tip of the triangle. But, since the triangle has its top sliced off, the legs end where the slice occurred.
The third word is altitude, which is simply the height of the trapezoid. It is how tall the trapezoid is when sitting on a flat surface. You can find the altitude by measuring straight across from one base to the other.
When your trapezoid's legs are the same length and when the angles each side forms with the bases are equal, then you have what is called an isosceles trapezoid. This means that, with the trapezoid sitting flat with the longest base down, the bottom two angles will be equal, and the top two angles will also be equal. Picture this kind of trapezoid as an isosceles triangle (a triangle with two equal sides and two equal angles) with its top cut off.
Now picture a scalene triangle (a triangle whose sides are all different lengths), and cut its top off. When you do this, you get a scalene trapezoid, a trapezoid whose legs are different lengths.
A third kind of special trapezoid is a right trapezoid, a trapezoid where one leg is perpendicular to the bases. It will look like a right triangle (a triangle with one right angle) with its top cut off.
Wow! Look at all we've learned in just a few short minutes! We've learned that a trapezoid is a four-sided flat shape with one pair of parallel sides. Trapezoids look like triangles with their tops cut off. The one property that all trapezoids must follow is that they must have two sides that are parallel to each other.
The special words we use with trapezoids are bases, legs, and altitude. Bases refer to the two sides that are parallel to each other. The legs refer to the two sloping sides, and altitude is simply the height of the trapezoid when it is sitting flat with its longest base down.
The special case of an isosceles trapezoid happens when you have the legs equal in length to each other, and the angles formed by the legs and bases are also equal to each other. So, an isosceles trapezoid will have the two bottom and the two top angles equal to each other. The special case of a scalene trapezoid happens when both legs are different lengths, and a right trapezoid occurs when you have one leg that is perpendicular to the bases.
Absorbing the information from this lesson could result in your ability to:
- Recognize the property associated with trapezoids
- Define bases, legs and altitude as they relate to trapezoids
- Characterize special trapezoids: isosceles, scalene and right