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# Classifying triangles

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

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.