## Quadrilateral properties | Perimeter, area, and volume | Geometry | Khan Academy

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.