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### Course: Basic geometry and measurement > Unit 4

Lesson 4: Classifying geometric shapes# Quadrilateral properties

Learn about the properties of quadrilaterals, parallelograms, trapezoids, rhombuses, rectangles, and squares. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- In4:49i realized that a rectangle cannot be a square, however a square can be a rectangle. Is this right?(416 votes)
- That is right because a square is a type of rectangle(262 votes)

- At around2:50, Sal goes on about the importance to clarify your definition of trapezoid. Does anyone have any examples of when or why someone would use the broader definition?(93 votes)
- To give one example, let's say that you proved the formula for the area of a trapezoid. Then you could easily find the area of a parallelogram IF you thought that it was a special kind of trapezoid where the two bases had the same length. There are a couple of other small sorts of things like that that could save you a little bit of thought.

As a mathematician, I think that anyone who is really passionate one way or the other about this needs to get out more. :)(114 votes)

- does a rectangle have to have two different pairs of side lengths or can it have 4 lengths that are the same?(22 votes)
- You are correct. Squares are also rectangles.(34 votes)

- What would a hundred sided shape be called a centagon?(20 votes)
- Actually they are called hectogons but centagon would also make sense.(20 votes)

- Which definition of a trapezoid would you guys pick? My choice is at least one pair of parallel. What's yours?(20 votes)
- A 4-sided flat shape with straight sides that has a pair of opposite sides parallel.(6 votes)

- what is the difference between a parallelogram and a trapezium ? :)(8 votes)
- Both
**parallelograms**and**trapeziums**are*quadrilaterals*.**Trapeziums**have*at least***one**couple of parallel opposite sides. (Some claim it is exactly one couple, but I prefer the broader definition)**Parallelograms**have**two**couples of parallel opposite sides. According to the definition I prefer, all**parallelograms**are*trapeziums*( but**not**all trapeziums are parallelograms ).(25 votes)

- What do the yellow tick marks/tiny lines on each side of the shape indicate?(11 votes)
- The squares on the corners indicate it is a right angle, meaning a 90 degree angle and the lines on the sides i think indicate if that side is parallel with its opposite side.(9 votes)

- A shape could have as many as a 10000000 sides right?(9 votes)
- There are shapes such as chilikagon with 1000 sides.

And 3d shapes such as myriagon with 10,000 sides.

There can be shapes liked that with 10000 or so sides but I have not heard of anything like that.(8 votes)

- Some rectangles are squares but not all and all squares are rectangles(10 votes)
- Not true, actually. Rectangles can't be squares, but squares can be rectangles because to definition of square is 4 equal sides and 4 right angles, while rectangles only have 4 right angles.(5 votes)

- a square is not always a retangle however it could be sometimes(8 votes)
- That doesn't sound right. A square has to have 4 right angles, which is the definition of a rectangle. So all squares are rectangles. However, not all rectangles are squares because squares have 4 sides of equal length (which means squares are rhombuses, too), and not all rectangles are rhombuses. Case in point: All squares are rectangles, but not all rectangles are squares.(2 votes)

## Video transcript

Which of the
following names can be used to describe the
geometric shape below? So the first name in
question is a quadrilateral. And a quadrilateral is
literally any closed shape that has four sides. And this is definitely a closed
shape that has four sides. So it is definitely
a quadrilateral. Next, we have to think about
whether it is a parallelogram. A parallelogram
is a quadrilateral that has two pairs of parallel
sides, where in each pair they're opposite sides. And in this case, if you
look at this side over here, it forms a 90-degree
angle with this line. And this side over here
also forms a 90-degree angle with this line over here. So these two sides are parallel. And then you could make
the exact same argument for the other two sides. This line up here forms a
90-degree angle with this side. And so does this side. It forms a 90-degree angle
with this line right over here. They form the same
angle with this line. They're parallel. So this side is parallel to
that side right over there. So this is definitely
also a parallelogram. Next, we ask about a trapezoid. Now, trapezoid is interesting. Sometimes a trapezoid is defined
as any quadrilateral having at least one pair
of parallel sides. Sometimes it's defined
as having only one pair of parallel sides. So let me write this down. Trapezoid, there's
a debate here. It's not completely settled. Some people say at least
one pair of parallel sides. That's one definition,
one possible definition. The other one is at exactly
one pair of parallel sides. How we answer this question
depends on which definition for trapezoid we pick. Now, the one that
people most refer to is actually this
one right over here, exactly one pair
of parallel sides. So when you think
of a trapezoid, they think of something like
this, where this side over here is parallel to
that side over here and those two are not parallel. But sometimes you'll also
see this at least one pair of parallel sides. And so this would
include parallelograms. It would be inclusive
of parallelograms because parallelograms have
two pairs of parallel sides. But I'm going to go with this
definition right over here, exactly one pair
of parallel sides. This has two pairs
of parallel sides so I will not call
it a trapezoid. But it's always important to
clarify what people are talking about because some
people might say a trapezoid is at least
one pair of parallel sides. And if we used that
definition, then we would call it a trapezoid. So it really depends on the
definition that you're using. Now, let's go on to rhombus. So a rhombus is a quadrilateral
where four of the sides are congruent. So a rhombus will
look like this. All four sides have
the same length. They're not necessarily at
right angles to each other. This figure over here,
we have two pairs of a size that are
the same length, but there's no
information that tells us that this side is
equal to that side or that this side is
equal to that side. So we can't make the claim that
this is necessarily a rhombus. We don't know for sure. If someone told us that this
length is equal to that length, then things change. But for the sake
of this one, we're not going to go with a rhombus. A rectangle is essentially
a parallelogram that has four right angles. And we already established
this is a parallelogram, and it also has four right
angles-- one, two, three, four. So this is a rectangle. Another way to think
about a rectangle is opposite sides
have the same length, and you have four right angles. So this is definitely
a rectangle. A square, a couple of way
you can think about a square. You could view a square as a
rhombus with four right angles . So if were to straighten it out
a little bit, it's a rhombus so all the four
sides are the same. And you have four right angles. That's one way to
think about a square. Or you could view
it as a rectangle where all four
sides are congruent. But in either case, you have
to have all four sides be congruent in order
to be a square. And we already established we
ruled out this being a rhombus, that all four sides here are
not necessarily congruent. You have two pairs
of congruent sides, but we don't know whether
this side and this side are congruent. So we cannot call this a square. So it's not a square,
not a rhombus, not a trapezoid by the
definition we picked, which is the less
inclusive version where you say exactly one
pair of parallel sides. It is a quadrilateral. It is a parallelogram. It is a rectangle.