Is a square always a rombus?

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!

is there any proof that if a parallelogram has one right angle, it's a rectangle?

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

soo, every shape with four sides is a quadriladeral?

If the sides are connected to each other and are straight, yes.

Im sure a kite is a quadrilateral that is shaped like a kite. You can search up different types of them.

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? :/

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.

What is a trapezoid and isosceles trapezoid?

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.

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5th grade

Course: 5th grade > Unit 16

Lesson 2: Quadrilaterals

Quadrilateral types

Name: Quadrilateral types
Uploaded: 2013-09-22T00:22:22Z
Description: Learn to identify quadrilaterals such as kites, trapezoids, parallelograms, rhombuses, rectangles, and squares by side length, presence of parallel sides, and angle type.

Google Classroom

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.

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DOGE
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Goezonme
Posted 4 years ago. Direct link to Goezonme's post “Is a square always a romb...”
Is a square always a rombus?
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Answer
- Polina Vitić
  Posted 4 years ago. Direct link to Polina Vitić's post “Yes, because a *rhombus* ...”
  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!
  Comment on Polina Vitić's post “Yes, because a *rhombus* ...”
  (14 votes)
Angel
Posted 4 months ago. Direct link to Angel's post “༎ຶ‿༎ຶ im fine ༎ຶ‿༎ຶ”
༎ຶ‿༎ຶ im fine ༎ຶ‿༎ຶ
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pcreativecrafter
Posted 8 years ago. Direct link to pcreativecrafter's post “is there any proof that i...”
is there any proof that if a parallelogram has one right angle, it's a rectangle?
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(6 votes)
Answer
- light city
  Posted 8 years ago. Direct link to light city's post “Well, the definiton of pa...”
  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
  Comment on light city's post “Well, the definiton of pa...”
  (2 votes)
meghatchanda
Posted 3 months ago. Direct link to meghatchanda's post “soo, every shape with fou...”
soo, every shape with four sides is a quadriladeral?
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Answer
- Hummingbird.
  Posted 3 months ago. Direct link to Hummingbird.'s post “If the sides are connecte...”
  If the sides are connected to each other and are straight, yes.
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Ian Salters
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please help me with this stuff
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Thunder
Posted 5 months ago. Direct link to Thunder's post “0:00What is the type of t...”
0:00
What is the type of this quadrilateral?
0:02
Be as specific as possible with the given data.
0:05
So it clearly is a quadrilateral.
0:07
We have four sides here.
0:09
And we see that we have two pairs of parallel sides.
0:13
Or we could also say there are two pairs of congruent sides
0:16
here as well.
0:17
This side is parallel and congruent to this side.
0:20
This side is parallel and congruent to that side.
0:23
So we're dealing with a parallelogram.
0:26
Let's do more of these.
0:29
So here it looks like a same type of scenario
0:31
we just saw in the last one.
0:32
We have two pairs of parallel and congruent sides,
0:35
but all the sides aren't equal to each other.
0:37
If they're all equal to each other,
0:38
we'd be dealing with a rhombus.
0:39
But here, they're not all equal to each other.
0:42
This side is congruent to the side opposite.
0:44
This side is congruent to the side opposite.
0:46
That's another parallelogram.
0:50
Now this is interesting.
0:52
We have two pairs of sides that are parallel to each other,
0:55
but now all the sides have an equal length.
0:58
So this would be a parallelogram.
1:00
And it is a parallelogram, but they're
1:02
saying to be as specific as possible with the given data.
1:05
So saying it's a rhombus would be
1:07
more specific than saying it's a parallelogram.
1:09
This does satisfy the constraints
1:11
for being a parallelogram, but saying it's a rhombus
1:13
tells us even more.
1:15
Not every parallelogram is a rhombus,
1:17
but every rhombus is a parallelogram.
1:19
Here, they have the sides are parallel to the side opposite
1:23
and all of the sides are equal.
1:26
Let's do a few more of these.
1:28
What is the type of this quadrilateral?
•Current transcript segment:
1:30
Be as specific as possible with the given data .
1:34
So we have two pairs of sides that are parallel,
1:37
or I should say one pair.
1:38
We have a pair of sides that are parallel.
1:41
And then we have another pair of sides that are not.
1:46
So this is a trapezoid.
1:48
But then they have two choices here.
1:49
They have trapezoid and isosceles trapezoid.
1:53
Now an isosceles trapezoid is a trapezoid
1:57
where the two non-parallel sides have the same length, just
2:00
like an isosceles triangle, you have
2:02
two sides have the same length.
2:04
Well we could see these two non-parallel sides do not
2:07
have the same length.
2:08
So this is not an isosceles trapezoid.
2:10
If they did have the same length, then
2:12
we would pick that because that would
2:13
be more specific than just trapezoid.
2:15
But this case right over here, this is just a trapezoid.
2:19
Let's do one more of these.
2:21
What is the type of this quadrilateral?
2:23
Well we could say it's a parallelogram
2:25
because all of the sides are parallel.
2:27
But if we wanted to be more specific,
2:28
you could also see that all the sides are the same.
2:31
So you could say it's a rhombus, but you
2:33
could get even more specific than that.
2:34
You notice that all the sides are
2:36
intersecting at right angles.
2:38
So this is-- if we wanted to be as specific as possible-- this
2:42
is a square.
2:45
Let me check the answer.
2:46
Got it right.
Button navigates to signup pageComment on Thunder's post “0:00What is the type of t...”
(5 votes)
Answer
Jason
Posted 8 years ago. Direct link to Jason's post “What is a kite?”
What is a kite?
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(4 votes)
Answer
- 『Lamiya』
  Posted 6 months ago. Direct link to 『Lamiya』's post “Im sure a kite is a quadr...”
  Im sure a kite is a quadrilateral that is shaped like a kite. You can search up different types of them.
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  (2 votes)
Kake
Posted 6 years ago. Direct link to Kake's post “What is a trapezoid and i...”
What is a trapezoid and isosceles trapezoid?
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(3 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “Imagine starting with a t...”
  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.
  Comment on David Severin's post “Imagine starting with a t...”
  (6 votes)
KhanAcademyUser
Posted 7 years ago. Direct link to KhanAcademyUser's post “Just a quick question tha...”
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? :/
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(4 votes)
Answer
- andrew26330
  Posted 7 years ago. Direct link to andrew26330's post “No. By definition trapezo...”
  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.
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  (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.