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Classifying triangles

Learn to categorize triangles as scalene, isosceles, equilateral, acute, right, or obtuse.  Created by Sal Khan.

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  • mr pants teal style avatar for user ultrabaymax
    What about reflex angles?
    (43 votes)
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  • piceratops seed style avatar for user SireeshaSom
    What if I had a isosceles triangle. Would it be a right angle?
    (15 votes)
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  • marcimus pink style avatar for user Khushi Kadecha
    Why is an equilateral triangle part of an icoseles triangle.
    (15 votes)
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    • blobby green style avatar for user hi
      I've asked a question similar to that.
      An equilateral triangle has all three sides equal, right?
      But on the other hand, we have an isosceles triangle, and the requirements for that is to have ONLY two sides of equal length. That's why.
      (16 votes)
  • piceratops seed style avatar for user SireeshaSom
    Are all triangles 180 degrees, if they are acute or obtuse?
    (10 votes)
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  • female robot ada style avatar for user Christy Han
    To remember the names of the scalene, isosceles, and the equilateral triangles, think like this!
    Scalene: I have no rules, I'm a scale! My weight are always different!
    Isosceles: I am an I (eye) sosceles (Isosceles)
    Equilateral: I'm always equal, I'm always fair!
    (15 votes)
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  • starky tree style avatar for user RYN&LYN
    What is a reflex angle? I've heard of it, and @ultrabaymax mentioned it. Maybe this is the wrong video to post this question on, but I'm really curious and I couldn't find any other videos on here that might match this question.
    (7 votes)
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  • blobby green style avatar for user bimbo oye
    Can an obtuse angle be a right.
    Can a acute be a right to.
    What type of isosceles triangle can be an equilateral.
    An isosceles triangle can not be an equilateral because equilateral have all sides the same,but isosceles only has two the same.
    (5 votes)
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    • primosaur ultimate style avatar for user Massimo
      An obtuse triangle cannot be a right triangle. A right triangle must have one angle equal to 90 degrees. All three of a triangle's angles always equal to 180 degrees, so, because 180-90=90, the remaining two angles of a right triangle must add up to 90, and therefore neither of those individual angles can be over 90 degrees, which is required for an obtuse triangle.

      An acute triangle can't be a right triangle, as acute triangles require all angles to be under 90 degrees. A right triangle has to have one angle equal to 90 degrees.

      All isosceles triangles are equilateral. The only requirement for an isosceles triangle is for at minimum 2 sides to be the same length. An isosceles triangle can have more than 2 sides of the same length, but not less. Equilateral triangles have 3 sides of equal length, meaning that they've already satisfied the conditions for an isosceles triangle.
      (8 votes)
  • mr pants teal style avatar for user Aziz Mohi
    so,every triangle has angles of 60 degrees and then they add up to 180 degrees?
    (2 votes)
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    • duskpin sapling style avatar for user by32782
      You're partly right.

      Yes, every triangle's 3 angles always add up to 180 degrees.

      But no, each angle does not have to be 60 degrees. Just as long as they each add up to 180 degrees, they're fine.

      So these are good:
      60, 60, 60
      70, 60, 50
      Even: 170, 5, 5

      But these aren't:
      70, 70, 70
      60, 60, 59
      180, 1, 1
      (10 votes)
  • male robot johnny style avatar for user bob the builder
    An equilateral triangle has all three sides equal?
    But on the other hand, we have an isosceles triangle, and the requirements for that is to have ONLY two sides of equal length.
    (6 votes)
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    • aqualine tree style avatar for user Mia
      An equilateral triangle has all three sides equal?
      Answer: Yes
      But on the other hand, we have an isosceles triangle, and the requirements for that is to have ONLY two sides of equal length.
      Answer: Yes, the requirement for an isosceles triangle is to only have TWO sides that are equal. (e.g, there is a triangle, two sides are 3cm, and one is 2cm. That is an isosceles triangle. An equilateral triangle would have all equal sides.).
      (0 votes)
  • leaf grey style avatar for user Arzal
    What is a perfect triangle classified as?
    (2 votes)
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Video transcript

What I want to do in this video is talk about the two main ways that triangles are categorized. The first way is based on whether or not the triangle has equal sides, or at least a few equal sides. Then the other way is based on the measure of the angles of the triangle. So the first categorization right here, and all of these are based on whether or not the triangle has equal sides, is scalene. And a scalene triangle is a triangle where none of the sides are equal. So for example, if I have a triangle like this, where this side has length 3, this side has length 4, and this side has length 5, then this is going to be a scalene triangle. None of the sides have an equal length. Now an isosceles triangle is a triangle where at least two of the sides have equal lengths. So for example, this would be an isosceles triangle. Maybe this has length 3, this has length 3, and this has length 2. Notice, this side and this side are equal. So it meets the constraint of at least two of the three sides are have the same length. Now an equilateral triangle, you might imagine, and you'd be right, is a triangle where all three sides have the same length. So for example, this would be an equilateral triangle. And let's say that this has side 2, 2, and 2. Or if I have a triangle like this where it's 3, 3, and 3. Any triangle where all three sides have the same length is going to be equilateral. Now you might say, well Sal, didn't you just say that an isosceles triangle is a triangle has at least two sides being equal. Wouldn't an equilateral triangle be a special case of an isosceles triangle? And I would say yes, you're absolutely right. An equilateral triangle has all three sides equal, so it meets the constraints for an isosceles. So by that definition, all equilateral triangles are also isosceles triangles. But not all isosceles triangles are equilateral. So for example, this one right over here, this isosceles triangle, clearly not equilateral. All three sides are not the same. Only two are. But both of these equilateral triangles meet the constraint that at least two of the sides are equal. Now down here, we're going to classify based on angles. An acute triangle is a triangle where all of the angles are less than 90 degrees. So for example, a triangle like this-- maybe this is 60, let me draw a little bit bigger so I can draw the angle measures. That's a little bit less. I want to make it a little bit more obvious. So let's say a triangle like this. If this angle is 60 degrees, maybe this one right over here is 59 degrees. And then this angle right over here is 61 degrees. Notice they all add up to 180 degrees. This would be an acute triangle. Notice all of the angles are less than 90 degrees. A right triangle is a triangle that has one angle that is exactly 90 degrees. So for example, this right over here would be a right triangle. Maybe this angle or this angle is one that's 90 degrees. And the normal way that this is specified, people wouldn't just do the traditional angle measure and write 90 degrees here. They would draw the angle like this. They would put a little, the edge of a box-looking thing. And that tells you that this angle right over here is 90 degrees. And because this triangle has a 90 degree angle, and it could only have one 90 degree angle, this is a right triangle. So that is equal to 90 degrees. Now you could imagine an obtuse triangle, based on the idea that an obtuse angle is larger than 90 degrees, an obtuse triangle is a triangle that has one angle that is larger than 90 degrees. So let's say that you have a triangle that looks like this. Maybe this is 120 degrees. And then let's see, let me make sure that this would make sense. Maybe this is 25 degrees. Or maybe that is 35 degrees. And this is 25 degrees. Notice, they still add up to 180, or at least they should. 25 plus 35 is 60, plus 120, is 180 degrees. But the important point here is that we have an angle that is a larger, that is greater, than 90 degrees. Now, you might be asking yourself, hey Sal, can a triangle be multiple of these things. Can it be a right scalene triangle? Absolutely, you could have a right scalene triangle. In this situation right over here, actually a 3, 4, 5 triangle, a triangle that has lengths of 3, 4, and 5 actually is a right triangle. And this right over here would be a 90 degree angle. You could have an equilateral acute triangle. In fact, all equilateral triangles, because all of the angles are exactly 60 degrees, all equilateral triangles are actually acute. So there's multiple combinations that you could have between these situations and these situations right over here.