Quadrilateral relationships: Trapezoids and parallelograms
About this video
The video decides whether a trapezoid is always, sometimes or never a parallelogram. Using the inclusive definition (a trapezoid has at least one pair of parallel sides), a parallelogram is always a trapezoid. But a trapezoid with only one pair of parallel sides is not a parallelogram, so a trapezoid is sometimes a parallelogram.
You'll be able to
- state the inclusive definition of a trapezoid.
- explain why a parallelogram is always a trapezoid under the inclusive definition.
- decide whether a statement about shapes is always, sometimes or never true.
Key words
- trapezoid
- A four-sided shape with at least one pair of parallel sides (inclusive definition).
- parallelogram
- A four-sided shape with two pairs of parallel sides.
- parallel
- Lines that go in the same direction and never meet.
- inclusive definition
- A definition that says 'at least', so shapes with more of the feature still count.
- exclusive definition
- A definition that says 'only', so shapes with more of the feature do not count.
Transcript
- [Instructor] So we're asked to complete the statement with always, sometimes or never. And it says, "A trapezoid is blank a parallelogram." And this is a screenshot from Khan Academy. So is a trapezoid always a parallelogram, is it sometimes a parallelogram or is it never a parallelogram?
So pause this video and have a go at this before we do this together. Okay, so let's just think about how these relate to each other. So the definition of a trapezoid that we are using on Khan Academy, this is oftentimes called the inclusive definition of a trapezoid, is at least, at least, one pair, pair, of parallel, parallel sides.
So what are examples based on that definition of a trapezoid? Well, you could have a trapezoid that looks like this. So let's say that side is parallel to that side. So that's one pair of parallel sides and a lot of people when they think about a trapezoid, they oftentimes think about something like this that has only one pair of parallel sides.
If we made that the definition, that would be the exclusive definition. But we're saying at least one pair of parallel sides. So it can also have two pairs of parallel sides. So we could also have this. So let's say that's our first pair of parallel sides right there, but then we could also have our second pair of parallel sides.
Pair of parallel sides, that's a tongue twister. So that's our second pair. And this right over here is a parallelogram. So a parallelogram has two pairs of parallel sides, but that meets the inclusive definition of a trapezoid that has at least one pair of parallel sides.
So a parallelogram is always going to be a trapezoid by this definition, but that's not the order here. They're saying a trapezoid. Well, sometimes it's not a parallelogram, but sometimes a trapezoid is a parallelogram. So what we want to go with this one is sometimes, a trapezoid is sometimes a parallelogram.
We see that right over here. This is not a parallelogram on the left, this is a parallelogram on the right, but these are both trapezoids.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.