Name: Math Antics - Triangles
Uploaded: 2016-07-22T17:35:04.000Z
Duration: 7 min 40 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

In this Geometry lesson,  we’re gonna learn all about triangles.

Modal verbs - B1

You may remember from the lesson about polygons   that triangles are special polygons

And that’s what the word ‘triangle’ means.

“tri" means 3 and “angles” means... angles.

Okay, that’s easy enough... 3 sides... 3 angles...

but what else is there to know about triangles?

Well for starters, we’re gonna learn how to classify triangles.

Oooo… such a classy triangle! [laughter]

But seriously, there’s two different way to classify (or organize) triangles.

They can be classified by their sides  and they can be classified by their angles.

Let’s start by classifying triangles by their angles

since we’ve already learned a lot about angles   in the previous videos.

You may remember from our first video about angles   that there’s 3 types of angles:

there’s right angles, acute angles, and obtuse angles.

And can you guess what these three different kinds of triangles are called?

So that’s simple enough.  But notice that for each of our three triangles,

the new angles that were formed  when we closed the shapes

So triangles always have at least 2 acute angles...

and it’s the other angle that determines what type it is.

That’s important to know so you don’t get tricked.

For any given triangle,  just because you see one acute angle,

that doesn't mean it’s an acute triangle.

You have to look at ALL the angles to tell if  it’s an acute triangle.

The situation is easier with right and obtuse triangles because you can only have ONE

So as soon as you spot one of those kinds of angles,

Alright then… classifying triangles by angles  is pretty simple.

But we can also classify triangles by their sides.

If we pay close attention  to the length of each side of a triangle,

we can see that there are three possibilities.

First of all, if all three sides of a triangle are exactly the same length,

then we call it an Equilateral Triangle.  It’s kind of  a long word, but it’s easy to remember

because it sounds like it has the word “equal” in it.

To see the second possibility, let’s take the top vertex of our equilateral triangle

and move it up like this. See what happened? Two of the triangle’s sides got stretched

by the same amount,  but the bottom side remained the same.

Now we have a triangle that has only 2 equal sides, and that’s called an Isosceles Triangle.

That’s a long word too. The best way to remember that is to look at an isosceles triangle

and say it’s name 20 times as fast as you can!

Is osceles, Isosceles, Isosceles, Isosceles,    Isosceles, Isosceles, Isosceles, Isosceles,...

And finally, to see the third possibility, let’s move that same top vertex again...

but this time to the left.  Now, all the sides are different lengths.

This type of triangle is called a Scalene Triangle.

So those are the three possibilities when classifying triangles by their sides.

Equilateral Triangles have 3 equal sides.

Isosceles triangles have only 2 equal sides.

And scalene triangles have NO equal sides.

That way was pretty easy too.  The hardest part is just remembering the names.

And now that you know both ways to classify triangles, let’s see how you can use them together.

Yep, you can use them both at the same time.

If you classify triangles both by their angles and by their sides,

it turns out that there's several possible combinations.

let’s list the three classifications by sides:  (scalene, isosceles, and equilateral)

…and the three classifications by angle: (right, acute and obtuse)

A scalene triangle can also be a right triangle,  like this one.

And a scalene triangle can also be  either an obtuse or an acute triangle.

In the same way, an isosceles triangle can also be acute, like this one,

And in one special case, an isosceles triangle can also be a right triangle, like so.

But things are different when it comes to an equilateral triangle.

An equilateral triangle is always an acute triangle.

Because all three sides are exactly the same,  all three angles must also be exactly the same.

And since we can’t have more than one right angle in a triangle, or more than one obtuse angle,

ALL the angles in an equilateral triangle must be acute.

Okay, now that you know all about how  triangles are classified,

let’s learn one more really important thing  about triangles.

In our video about angles and degrees, we learned that we can measure angles and say

how big or how small they are using special units called degrees.

Well, since triangles are always made up of 3 angles,

each of those angles has its own  measurement in degrees.

And the important thing  is that those three angle measurements,

if you combine them, they will always  add up to 180 degrees.

For example, have a look at this triangle. If we were to take a saw and cut it up into

three separate angles, ...and then if we were to take those three angles and rearrange them

so that they’re right next to each other like this,

you can see that the total would be the same as a straight angle... that’s 180 degrees!

And this will work no matter what type of triangle it is.

Knowing that a triangle’s angles will  always add up to 180 degrees can

really help you out when solving geometry problems.

There’s a whole lot of situations where you’ll know what two of the angles are,

but you need to figure out what the third angle is. Like in this problem.

With this triangle, we’re told that one of the angles is 35 degrees,

and the other is 45 degrees. But the third angle is unknown. We need to figure out what it is.

Since we know that the total must be 180 degrees,

we can just add up the angles that we DO know,