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# Worked example: Classifying triangles

Video transcript

Categorize the following
triangles according to whether or not they
are obtuse triangles. So an obtuse triangle
is a triangle that has an obtuse
angle in it, or an angle that is larger than 90 degrees. So it's pretty clear
that this one does not have any obtuse angles. This is a 90 degree
angle, and these are going to have to be
less than 90 degrees. So this is not obtuse. This one right over here,
just by looking at it, you see that all of them
are less than 90 degrees, so I'll put this not obtuse. Now, these two are interesting. Angle JKL looks like it
is larger than 90 degrees, and we can assume that
these are drawn to scale, so we can base it on
our visual judgment. So I would say that
this is obtuse, and angle BAC also looks like
it is larger than 90 degrees. So that's an obtuse
angle, so I would throw that in the
obtuse bucket as well. So we had two not
obtuse, two obtuse. Check our answer. Let's do a couple more of these. Which of the following
are correct descriptions of triangle PIG? Or I guess triangle pig? Select all that apply. PIG is equilateral. Well, that's not true. To be equilateral, all the sides
have to be the same length. And we see here two
sides are seven, but one side has length 4. So that's not true. Angle PIG has two equal angles. Well, we see that
right over here, these two angles
that are 74 degrees. So that's true. Triangle PIG, I guess,
has an obtuse angle. Well, an obtuse angle is one
that's larger than 90 degrees. None of these are
larger than 90. That's not true. Triangle PIG has
three acute angles. Well, that is true. All of these angles are
less than 90 degrees. Triangle PIG has a right angle. No, none of these angles
are exactly 90 degrees, so it does not
have a right angle. So let's check our answer. Let's do one more of this. This is actually kind of fun. Categorize the following
triangles according to whether or not they
are equilateral. So to be equilateral,
all of the sides have to have the same length. So this is equilateral. This one, the sides are
definitely not the same length. In fact, not even two of the
sides are the same length. That's really a
scalene triangle. Here we have two sides
that are the same length, but the third is different. This would be an
isosceles triangle, but it's not equilateral. And here they're
all the same length, so we have an
equilateral triangle. We got it right.