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### Course: Basic geometry and measurement>Unit 4

Lesson 6: More on 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?

• Is a square always a rombus?
(18 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!
(24 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? :/
(5 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.
(7 votes)
• is there any proof that if a parallelogram has one right angle, it's a rectangle?
(7 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?
(6 votes)
• Yeah, quad means 4. To be a quadrilateral, it HAS to have no curves AND be a closed shape.
(1 vote)
• is a square always a rhombus ?
(5 votes)
• A square is defined as a quadrilateral with 4 equal sides and 4 equal angles.

A rhombus is defined as a quadrilateral with 4 equal sides.

Comparing these definitions, we see that, yes, every square is a rhombus. However, not every rhombus is a square (for example, think of a tall and thin diamond shape).
(5 votes)
• i am still confused.for example,at why did you choose like the rhombus instead of the parallelogram.
(4 votes)
• He picked rhombus instead of parallelogram because rhombus is the most specific item from the list. The question asks for us to "be as specific as possible" so while it is a parallelogram, that answer would be wrong.
Rhombus is more specific because rhombi are a subset of parallelograms, meaning all rhombi are parallelograms, but not all parallelograms are rhombi. Rhombus is a parallelogram with all equal sides.
(6 votes)
• What is a trapezoid and isosceles trapezoid?
(4 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)
• How come the exercises claim that if every side has the same length, the quadrilateral has to be a rectangle? I was always taught only a square had all four sides of the same length and rectangles had two sets of parallels that differed in length.
(5 votes)
• what does "the given data" mean?
(3 votes)
• It means the data that is already there or the data that is included in the question.
(5 votes)
• If a quadrilateral has 4 equal sides, then it must be a _________?
- would the answer be a rhombus, square, or both?
(2 votes)
• rhombus first, because a square is a particular type of rhombus
(6 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.