Triangles: using angles to categorize | 4th grade | Khan Academy

Triangles: using angles to categorize | 4th grade | Khan Academy


Voiceover: We’ve already
seen that we can categorize triangles as being equilateral,
isoceles, or scalene based on the lengths of
the sides of the triangle. So, if none of the lengths are congruent, if you have something like this, we would consider this scalene. I am assuming that this side
is not equal to that side and neither of these
are equal to that side. So that would be scalene,
and this is all review. If I have at least two
of the sides being equal, so let’s say that side is the same length as that side right over there, so I’ll mark it off as
these are the same length, this would be an isosceles triangle. Then if all three of them, all
three sides, are congruent, if all three sides are the same length, we would call this equilateral. And in most circles, you could
also say this is isosceles because isosceles would be at
least two sides being equal. So this one definitely
has at least two sides, it has all three. So this is, you could say,
equilateral and isosceles. While this one, if we
assume this third side is a different length, this would just be
isosceles, not equilateral. Now all of that is review. Now, what I want to
think about in this video is well what if we’re not
given the lengths of the sides and what if we’re just
given a few of the angles. So, for example, let’s say
we were given a triangle. Let’s say that we were given a triangle where we’re given a few
of the angle measures. So let’s say we are told that
this angle right over here is 40 degrees and this angle
right over here is 50 degrees. Now, based on that, could
you somehow classify this as scalene,
isosceles, or equilateral? Well, the key here to
realize is if you know two interior angles of a
triangle you can always figure out the third because the three need to add up to 180 degrees. So if this is 40 and that is
50, these two add up to 90. So to add up to 180 degrees, this one must be a 90-degree angle. We can even mark it as a right angle. So if you have a triangle where
all of the interior angles are different, that means that all of the side lengths are going to be different. One way to think about it
is if this angle became wider, then this length
would have to become wider. If this angle became larger or smaller, then this side is going to have
to become larger or smaller. If this angle became larger or smaller, then this side is going to
become larger or smaller. So hopefully you
appreciate that if you have three different angles
you are going to have three different side lengths. So just based on the angles here, that we have three different angles, we can say that this is going
to be a scalene triangle. Now we can look at a
couple other examples. Let’s do an interesting one. Let’s say this angle right
over here is 70 degrees and let’s say this angle
over here is 40 degrees. Now, based on the
information I have given you, what kind of a triangle
is this going to be? Can you even figure it out? Well, we use the same idea. The interior angles need to add up to 180. 70 plus 40 is 110, so
you can say 110 plus what is equal to 180 degrees? Well, this is going to
have to be 70 degrees. So this angle right
over here is 70 degrees. So now we have a scenario
where two of the angles have the same measure. One way to think about it, based on whether this
angle is large or small, Is going to define the length of that side and this angle right over here, depending on how large or small it is, is going to define the
length on this side. So because these two angles are congruent, because they have the same measure, their opposite sides are
going to be congruent. So this is going to be the same as that. So just based on the information
I had started giving you, because you can show that two angles are going to be the same, you can say that this is going to be an isosceles triangle. Now let’s do a third example,
and you could probably guess what I am going to do
in this third example. Let’s say this angle is 60 degrees. What type of a triangle
is this going to be? Well, if this is 60 and this is 60, to make them add up to 180, that would have to be 60 degrees as well. If you have all of the angles congruent, that means that all of
the sides are congruent and so now you are dealing
with an equilateral. Now, as we said before,
also you can view this as a subset as isosceles
because you have at least two angles and you have
two sides being congruent, but here it is all three, so this is an equilateral triangle.

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