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Use these videos to add information to your sketchnote. You should include classification by angles (acute, obtuse, right) and by side length (equilateral, isosceles, and scalene). You should also include information about the sum of the interior angles of a triangle.

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Check out this tutorial for information on the different classifications of triangles.

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Classifying Triangles

If we want to classify triangles, there's no better expert than Goldilocks. You remember Goldilocks, right? She's the girl who broke into a home owned by some bears, stole some porridge, slept in several beds, and then fled when the bear homeowners returned.

Well, after serving some jail time (bears are rather litigious), Goldilocks gave up her life of crime and is here to help us by using her unique expertise with things that come in threes, like triangles.

Triangles, of course, are two dimensional shapes with three sides and three angles. But like bowls of porridge, not all triangles are the same. Let's let Goldilocks teach us more.

Scalene Triangles

The first way we classify triangles is based on their sides. There are three kinds of these triangles to know.

First, there's this triangle:

Goldilocks doesn't much like this triangle. None of the sides are equal in length. Since there is a direct correlation between the sides and the angles opposite the sides, there also aren't any equal angles. This is like a cold bowl of porridge, all around uneven. It's also a scalene triangle.

A scalene triangle is a triangle with no equal sides or angles. The word 'scalene' actually means uneven or unequal. Imagine uneven scales. As for Goldilocks, she remembers scalene triangles by remembering how gross cold porridge is. If there was a word for that clumpy, icky stuff, it might be scalene.

Isosceles Triangles

Then there's this triangle:

Notice those hash marks on two of the sides. That means the sides are congruent. This is an isosceles triangle. An isosceles triangle is a triangle with two equal sides and two equal angles.

Goldilocks likens this one to a hot bowl of porridge. It's not perfect, but it's not bad. With an isosceles triangle, there's nice symmetry.

Plus, if you know one angle, you know them all. In the triangle below, we know one bottom angle is 70 degrees. Since the two sides are congruent, the angles opposite them are also congruent, making the other bottom angle also 70 degrees. And since the sum of the interior angles of a triangle is 180 degrees, the final angle is 40 degrees.

Equilateral Triangle

Then we get to this equilateral triangle:

An equilateral triangle is a triangle with three equal sides and three equal angles. Think 'equal' to remember 'equilateral.' Since all the angles must add up to 180 degrees, each angle in an equilateral triangle is just 180 divided by 3, or 60 degrees. This is Goldilocks' favorite triangle. It's like that perfect bowl of porridge. Everything is just right.

Acute Triangles

Scalene, isosceles and equilateral are three classifications of triangles, but there's another way to label these shapes that's solely based on their angles.

Goldilocks thinks of these like those beds she tested at the bears' house. This first one, seen below, is all pointy and uncomfortable. We call it an acute triangle. A triangle is acute if all angles are less than 90 degrees.

Now, you can combine names. Remember our equilateral triangle? That was also acute. And the isosceles triangle we looked at? Also acute.

Obtuse Triangles

Here's the opposite of an acute triangle:

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classifying triangles by angles and sides - video & lesson transcript | study.com

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Classifying Triangles by Angles and Sides - Video & Lesson Transcript | Study.com

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If we want to classify triangles, there's no better expert than Goldilocks. You remember Goldilocks, right? She's the girl who broke into a home owned by some bears, stole some porridge, slept in several beds, and then fled when the bear homeowners returned.

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Check out this video for more information on the classifications by triangles.

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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.

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Classifying triangles (video) | Shapes | Khan Academy

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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.

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A triangle has three angles but the relationship between these angles is special. Watch this tutorial to find out more.

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A Triangle

If you cut a rectangular piece of cake in half diagonally, you will end up with two triangles. In this video lesson, we will talk about the angles of a triangle and why they always add up to 180 degrees. We can define a triangle as a flat shape with three straight sides.

Three Angles

The angles of the triangle are the inside corners of a triangle. You can see that there are three of them. No matter what size or kind of triangle you have, you will always have your three angles. Do you see the three angles in all of these triangles? We can label our three angles as a, b, and c. It doesn't matter which one we label which as long as all three are labeled.

The Formula and Proof

With our angles labeled, we have a formula we can refer to for the angles. It is a + b + c = 180, which tells us that if we add up all of our angles, they will always equal 180.

Why is this? Well, we can prove this with the use of parallel lines. If we extended the line between angles a and b and we drew a line through the tip of angle c that is parallel to the line going through the point of angles a and b, then we will see that all three angles add up to 180 degrees.

If you look at the parallel lines we've drawn and you compare the angles, you will see that angles a and b are the same angles as the angles on either side of angle c. Each side of the triangle becomes the line that intersects the pair of parallel lines, and because of this, the angles that are inside the parallel lines and on opposite sides of the intersecting line are equal.

Another way you can check this is to draw a triangle using a ruler. Then cut it out and then tear each angle off. Then connect the angles. What do they form? Don't they form a straight line at the bottom? This is the same kind of proof as the parallel lines proof. It shows you that all three angles always add up to 180 degrees, or a straight line.

Finding a Missing Angle

Because all triangles add up to 180 degrees, we can use this fact to our advantage. Sometimes we will have a triangle for which we know the measurement of two of the angles. The unknown third angle is easy to find since we know that all of them added up will equal 180. To find the missing angle, we can either use the formula and a bit of algebra or simply subtract the two known angles from 180 to find the unknown third.

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measuring the angles of triangles: 180 degrees - video & lesson transcript | study.com

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Measuring the Angles of Triangles: 180 Degrees - Video & Lesson Transcript | Study.com

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If you cut a rectangular piece of cake in half diagonally, you will end up with two triangles. In this video lesson, we will talk about the angles of a triangle and why they always add up to 180 degrees. We can define a triangle as a flat shape with three straight sides.

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Watch this video for an example problem (and solution) on finding angles within triangles.

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Learn about the angles in a triangle and a little about exterior angles being the sum of the remote interior angles.