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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.

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  • female robot ada style avatar for user Meghu
    In i realized that a rectangle cannot be a square, however a square can be a rectangle. Is this right?
    (3 votes)
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    • leaf red style avatar for user cassf16
      "In i realized that a rectangle cannot be a square, however a square can be a rectangle. Is this right?" Your statement before your question is not worded correctly. A square is always a rectangle, by definition. However, not all rectangles are squares. A square is the unique case of a rectangle also having 4 sides with the same length.
      (22 votes)
  • starky tree style avatar for user haaris
    a square is not always a retangle however it could be sometimes
    (7 votes)
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  • hopper cool style avatar for user ray  ( ͡° ͜ʖ ͡°) ✍(◔◡◔)
    can you vote this up please and thank you


    goal: <250
    (8 votes)
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  • male robot hal style avatar for user smathew
    A shape could have as many as a 10000000 sides right?
    (2 votes)
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    • male robot hal style avatar for user Sam
      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.
      (5 votes)
  • old spice man blue style avatar for user Kush Desai
    Which definition of a trapezoid would you guys pick? My choice is at least one pair of parallel. What's yours?
    (2 votes)
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  • leaf blue style avatar for user TB
    What do the yellow tick marks/tiny lines on each side of the shape indicate?
    (2 votes)
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    • male robot hal style avatar for user Sam
      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.
      (3 votes)
  • blobby green style avatar for user Omi
    Is there any differences between a trapezoid and a trapezium?
    Or are they same?
    (5 votes)
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  • orange juice squid orange style avatar for user Abrams, Cameron
    I don't get how a square is a rectangle but a rectangle isn't a square. They are two different shapes so how can they be the same.
    (5 votes)
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    • primosaur ultimate style avatar for user avisarus
      It's all about the formal definitions of the shapes. A rectangle is a 4-sided figure, with 4 right angles, and 2 sets of parallel lines. A square also fits this definition. A square is all the things a rectangle is, but with the added condition that all the sides need to be the same length.

      This makes all squares rectangles, but no rectangles are squares.
      (1 vote)
  • old spice man green style avatar for user Shazib Howlader
    What's the meaning of #congruent here. Sal uses this word I searched this but it didn't make sense to me. Can someone please explain the meaning of #congruent that Sal uses here?
    (2 votes)
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    • female robot amelia style avatar for user Johanna
      “Congruent” means that two things are the same size and shape.

      For example:
      If you had a circle and a smaller circle, those wouldn’t be congruent because they’re not the same size. If you had a triangle and a square that both had an area of 9 square units, they wouldn’t be congruent because they’re different shapes. If you have two regular hexagons that have side lengths of 3 units, those would be congruent.
      (6 votes)
  • male robot hal style avatar for user smathew
    Can a rectangle be a square or can a square be a rectangle or both?
    (3 votes)
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    • aqualine ultimate style avatar for user Skyguy
      Good question! The rectangle subgroup encompasses, or includes, the square subgroup. That means that if a quadrilateral is a square, then it is a rectangle. However, the opposite is not always true. Just because a quadrilateral is a rectangle, that does not prove that that quadrilateral is also a square. Note that a rectangle CAN also be a square, but does not have to be.

      To conclude, a square is always a rectangle, but a rectangle is not always a square.
      (4 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.