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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Not all triangles are the same. There are equilateral, isosceles and scalene triangles. Then there are right, acute and obtuse triangles. In this lesson, we'll learn how to classify triangles using their sides and angles.

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.

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.

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.

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.

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.

Here's the opposite of an acute triangle:

This one's obtuse. We call a triangle **obtuse** if one angle is more than 90 degrees. Of course, since our angles add up to 180 degrees, you can't have more than one angle that's more than 90 degrees. So, you only need one angle over 90 degrees to be obtuse.

How can you remember acute vs. obtuse? Well, an acute pain is a sharp, intense pain. An acute triangle forms a sharp angle, just like that uncomfortable bed. And if someone is obtuse, they're being dull or, well, not bright or sharp.

Just like an obtuse person is soft in the head, so to speak, Goldilocks thinks this bed's too soft. She's very particular about beds and triangles.

Note that you can't have an equilateral obtuse triangle. You can have an isosceles obtuse triangle. And the one we were first looking at here was not only obtuse, but also scalene.

Finally, we have a right triangle. And, yep, Goldilocks thinks this one is just 'right' for sleeping. A **right** triangle has one 90 degree angle.

So, acute triangles have angles that are all less than 90, obtuse triangles have an angle over 90, and right triangles have that magical 90 degree angle. It's just the 'right' angle for a bed.

Note that this blue one is scalene:

And, again, you can't have an equilateral right triangle. You can have an isosceles one. If one angle is 90, what are the other two angles? 45.

In summary, we helped Goldilocks avoid returning to a life of crime by helping us classify triangles.

We looked at scalene triangles, where all the sides and angles are different. Then there are isosceles triangles, where two sides and angles are equal. Next were equilateral triangles, where all sides and angles are equal. The angles in an equilateral triangle are always 60 degrees.

Our next three types of triangles were based just on angles. There are acute triangles, where all angles are less than 90 degrees. Then there are obtuse triangles, where one angle is more than 90 degrees. And if one angle is 90 degrees, we call it a right triangle.

After this lesson, you should have the ability to:

- Identify the properties of scalene, isosceles and equilateral triangles
- Describe how triangles can be classified based on angles

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Geometry: High School15 chapters | 160 lessons

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- Constructing Triangles: Types of Geometric Construction 5:59
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