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## Class 9 (Old)

### Course: Class 9 (Old) > Unit 7

Lesson 1: Kinds of quadrilaterals# Quadrilateral types

Learn to identify quadrilaterals such as kites, trapezoids, parallelograms, rhombuses, rectangles, and squares by side length, presence of parallel sides, and angle type. Created by Sal Khan.

## Want to join the conversation?

- upvote pls! help me earn a badge!(35 votes)
- Is a square always a rombus?(11 votes)
- Yes, because a
**rhombus**is a parallelogram with equal sides, and a**square**is*also*a parallelogram with equal sides.

The difference is that the square also has four right angles.**Rhombus**

- 4 equal sides

- parallelogram**Square**

- 4 equal sides

- parallelogram

- 4 equal 90° angles

Notice that the square - by definition - always meets the criteria for a rhombus. So*every*square is*also*a rhombus!

However, not every rhombus is a square: if the rhombus has 2 acute angles and 2 obtuse angles, then it is just a rhombus.

Hope this helps!(14 votes)

- ༎ຶ‿༎ຶ im fine ༎ຶ‿༎ຶ(7 votes)
- is there any proof that if a parallelogram has one right angle, it's a rectangle?(6 votes)
- Well, the definiton of parallelogram is that both pairs of sides are parallel - what I mean by pairs of sides is tricky to explain without a drawing, so I'm gong to assume you already know it. The diefinition of right angle is a measure of 90 deg, which means the two lines are perpendicular to each other. So with some logic you can see that if one line a is perpendicular to line b, and line c is parallel to line a, then line b has to be perpendicular to c as well. Right? And that means the angle between b and c has to be a right angle as well. You can keep going around the parallelogram and get four right angles, which means it's a rectangle(2 votes)

- soo, every shape with four sides is a quadriladeral?(5 votes)
- If the sides are connected to each other and are straight, yes.(3 votes)

- please help me with this stuff(6 votes)
- 0:00What is the type of this quadrilateral?0:02Be as specific as possible with the given data.0:05So it clearly is a quadrilateral.0:07We have four sides here.0:09And we see that we have two pairs of parallel sides.0:13Or we could also say there are two pairs of congruent sides0:16here as well.0:17This side is parallel and congruent to this side.0:20This side is parallel and congruent to that side.0:23So we're dealing with a parallelogram.0:26Let's do more of these.0:29So here it looks like a same type of scenario0:31we just saw in the last one.0:32We have two pairs of parallel and congruent sides,0:35but all the sides aren't equal to each other.0:37If they're all equal to each other,0:38we'd be dealing with a rhombus.0:39But here, they're not all equal to each other.0:42This side is congruent to the side opposite.0:44This side is congruent to the side opposite.0:46That's another parallelogram.0:50Now this is interesting.0:52We have two pairs of sides that are parallel to each other,0:55but now all the sides have an equal length.0:58So this would be a parallelogram.1:00And it is a parallelogram, but they're1:02saying to be as specific as possible with the given data.1:05So saying it's a rhombus would be1:07more specific than saying it's a parallelogram.1:09This does satisfy the constraints1:11for being a parallelogram, but saying it's a rhombus1:13tells us even more.1:15Not every parallelogram is a rhombus,1:17but every rhombus is a parallelogram.1:19Here, they have the sides are parallel to the side opposite1:23and all of the sides are equal.1:26Let's do a few more of these.1:28What is the type of this quadrilateral?

•Current transcript segment:1:30Be as specific as possible with the given data .1:34So we have two pairs of sides that are parallel,1:37or I should say one pair.1:38We have a pair of sides that are parallel.1:41And then we have another pair of sides that are not.1:46So this is a trapezoid.1:48But then they have two choices here.1:49They have trapezoid and isosceles trapezoid.1:53Now an isosceles trapezoid is a trapezoid1:57where the two non-parallel sides have the same length, just2:00like an isosceles triangle, you have2:02two sides have the same length.2:04Well we could see these two non-parallel sides do not2:07have the same length.2:08So this is not an isosceles trapezoid.2:10If they did have the same length, then2:12we would pick that because that would2:13be more specific than just trapezoid.2:15But this case right over here, this is just a trapezoid.2:19Let's do one more of these.2:21What is the type of this quadrilateral?2:23Well we could say it's a parallelogram2:25because all of the sides are parallel.2:27But if we wanted to be more specific,2:28you could also see that all the sides are the same.2:31So you could say it's a rhombus, but you2:33could get even more specific than that.2:34You notice that all the sides are2:36intersecting at right angles.2:38So this is-- if we wanted to be as specific as possible-- this2:42is a square.2:45Let me check the answer.2:46Got it right.(5 votes) - Im sure a kite is a quadrilateral that is shaped like a kite. You can search up different types of them.(2 votes)

- What is a trapezoid and isosceles trapezoid?(3 votes)
- Imagine starting with a triangle and cutting off the top parallel to the base of the triangle. That gives you a trapezoid which could be defined as a quadrilateral with exactly one set of parallel lines. Now if you start with an isosceles triangle with the base being the non-equal side, do the same thing and the two non-parallel sides are also congruent, so you have an isosceles trapezoid.

Trapezoids have different definitions and meanings depending on where you are in the world and which Math definition you choose. In Great Britain, what Americans call a trapezoid is called a trapezium (see http://mathworld.wolfram.com/Trapezium.html for some history), and an alternate definition of exactly one pair of parallel sides is given as AT LEAST one pair of parallel sides which would put all parallelograms under this definition. Sorry for the added confusion, but that is where Math is with the term.(6 votes)

- Just a quick question that's been on my mind:

Is it possible for any trapezoid to have the pair of parallel sides having equal length? If it did, it would be considered a square, right? But is a square considered a trapezoid? :/(4 votes)- No. By definition trapezoids will always have only one pair of parallel sides. Having a trapezoid with two parallel sides of equal length would give you two pairs of parallel sides, which would be considered a rectangle instead of a trapezoid. A square will also always have two pairs of parallel sides, and thus cannot be a trapezoid.(4 votes)

## Video transcript

What is the type of
this quadrilateral? Be as specific as possible
with the given data. So it clearly is
a quadrilateral. We have four sides here. And we see that we have two
pairs of parallel sides. Or we could also say there are
two pairs of congruent sides here as well. This side is parallel and
congruent to this side. This side is parallel and
congruent to that side. So we're dealing
with a parallelogram. Let's do more of these. So here it looks like
a same type of scenario we just saw in the last one. We have two pairs of
parallel and congruent sides, but all the sides aren't
equal to each other. If they're all
equal to each other, we'd be dealing with a rhombus. But here, they're not
all equal to each other. This side is congruent
to the side opposite. This side is congruent
to the side opposite. That's another parallelogram. Now this is interesting. We have two pairs of sides that
are parallel to each other, but now all the sides
have an equal length. So this would be
a parallelogram. And it is a
parallelogram, but they're saying to be as specific as
possible with the given data. So saying it's a
rhombus would be more specific than saying
it's a parallelogram. This does satisfy
the constraints for being a parallelogram,
but saying it's a rhombus tells us even more. Not every parallelogram
is a rhombus, but every rhombus
is a parallelogram. Here, they have the sides are
parallel to the side opposite and all of the sides are equal. Let's do a few more of these. What is the type of
this quadrilateral? Be as specific as possible
with the given data . So we have two pairs of
sides that are parallel, or I should say one pair. We have a pair of sides
that are parallel. And then we have another
pair of sides that are not. So this is a trapezoid. But then they have
two choices here. They have trapezoid and
isosceles trapezoid. Now an isosceles
trapezoid is a trapezoid where the two non-parallel
sides have the same length, just like an isosceles
triangle, you have two sides have the same length. Well we could see these two
non-parallel sides do not have the same length. So this is not an
isosceles trapezoid. If they did have the
same length, then we would pick that
because that would be more specific
than just trapezoid. But this case right over here,
this is just a trapezoid. Let's do one more of these. What is the type of
this quadrilateral? Well we could say
it's a parallelogram because all of the
sides are parallel. But if we wanted to
be more specific, you could also see that
all the sides are the same. So you could say it's
a rhombus, but you could get even more
specific than that. You notice that
all the sides are intersecting at right angles. So this is-- if we wanted to be
as specific as possible-- this is a square. Let me check the answer. Got it right.