| by Kenneth Chase | No comments

## 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
literally any closed shape that has four sides. And this is definitely a closed
shape that has four sides. So it is definitely
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.