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0:07 Hi! Welcome to Math Antics.

0:09 In this Geometry lesson, we’re gonna learn all about triangles.

0:13 You may remember from the lesson about polygons that triangles are special polygons

0:18 that always have 3 sides and 3 angles.

0:21 And that’s what the word ‘triangle’ means.

0:23 “tri" means 3 and “angles” means... angles.

0:28 Okay, that’s easy enough... 3 sides... 3 angles...

0:31 but what else is there to know about triangles?

0:34 Well for starters, we’re gonna learn how to classify triangles.

0:38 Oooo… such a classy triangle! [laughter]

0:42 But seriously, there’s two different way to classify (or organize) triangles.

0:47 They can be classified by their sides and they can be classified by their angles.

0:53 Let’s start by classifying triangles by their angles

0:56 since we’ve already learned a lot about angles in the previous videos.

1:00 You may remember from our first video about angles that there’s 3 types of angles:

1:05 there’s right angles, acute angles, and obtuse angles.

1:08 Well... watch what happens if we use

1:11 a third line in each of these angles

1:13 to form closed shapes.

1:14 Ah ha!… triangles!

1:17 And can you guess what these three different kinds of triangles are called?

1:20 Yep - The one made from the right angle

1:23 is called a Right Triangle.

1:25 The one made from the acute angle

1:26 is called an Acute Triangle,

1:29 and the one made from the obtuse angle

1:30 is called an Obtuse Triangle.

1:33 So that’s simple enough. But notice that for each of our three triangles,

1:37 the new angles that were formed when we closed the shapes

1:41 are all acute angles.

1:43 So triangles always have at least 2 acute angles...

1:47 and it’s the other angle that determines what type it is.

1:51 That’s important to know so you don’t get tricked.

1:53 For any given triangle, just because you see one acute angle,

1:57 that doesn't mean it’s an acute triangle.

1:59 You have to look at ALL the angles to tell if it’s an acute triangle.

2:03 The situation is easier with right and obtuse triangles because you can only have ONE

2:08 right or obtuse angle per triangle.

2:11 So as soon as you spot one of those kinds of angles,

2:14 you know what type of triangle you have.

2:17 Alright then… classifying triangles by angles is pretty simple.

2:21 But we can also classify triangles by their sides.

2:25 If we pay close attention to the length of each side of a triangle,

2:29 we can see that there are three possibilities.

2:32 First of all, if all three sides of a triangle are exactly the same length,

2:36 then we call it an Equilateral Triangle. It’s kind of a long word, but it’s easy to remember

2:41 because it sounds like it has the word “equal” in it.

2:44 To see the second possibility, let’s take the top vertex of our equilateral triangle

2:50 and move it up like this. See what happened? Two of the triangle’s sides got stretched

2:55 by the same amount, but the bottom side remained the same.

3:00 Now we have a triangle that has only 2 equal sides, and that’s called an Isosceles Triangle.

3:05 That’s a long word too. The best way to remember that is to look at an isosceles triangle

3:10 and say it’s name 20 times as fast as you can!

3:13 Isosceles, Isosceles, Isosceles, Isosceles, Isosceles, Isosceles, Isosceles, Isosceles,...

3:17 And finally, to see the third possibility, let’s move that same top vertex again...

3:22 but this time to the left. Now, all the sides are different lengths.

3:26 This type of triangle is called a Scalene Triangle.

3:31 So those are the three possibilities when classifying triangles by their sides.

3:35 Equilateral Triangles have 3 equal sides.

3:39 Isosceles triangles have only 2 equal sides.

3:43 And scalene triangles have NO equal sides.

3:46 That way was pretty easy too. The hardest part is just remembering the names.

3:51 And now that you know both ways to classify triangles, let’s see how you can use them together.

3:56 Yep, you can use them both at the same time.

3:59 If you classify triangles both by their angles and by their sides,

4:03 it turns out that there's several possible combinations.

4:06 To see what I mean,

4:08 let’s list the three classifications by sides: (scalene, isosceles, and equilateral)

4:14 …and the three classifications by angle: (right, acute and obtuse)

4:21 A scalene triangle can also be a right triangle, like this one.

4:25 And a scalene triangle can also be either an obtuse or an acute triangle.

4:31 In the same way, an isosceles triangle can also be acute, like this one,

4:36 or obtuse, like this one.

4:38 And in one special case, an isosceles triangle can also be a right triangle, like so.

4:45 But things are different when it comes to an equilateral triangle.

4:49 An equilateral triangle is always an acute triangle.

4:52 Because all three sides are exactly the same, all three angles must also be exactly the same.

4:59 And since we can’t have more than one right angle in a triangle, or more than one obtuse angle,

5:04 ALL the angles in an equilateral triangle must be acute.

5:08 Okay, now that you know all about how triangles are classified,

5:12 let’s learn one more really important thing about triangles.

5:16 In our video about angles and degrees, we learned that we can measure angles and say

5:21 how big or how small they are using special units called degrees.

5:26 Well, since triangles are always made up of 3 angles,

5:30 each of those angles has its own measurement in degrees.

5:33 And the important thing is that those three angle measurements,

5:37 if you combine them, they will always add up to 180 degrees.

5:43 For example, have a look at this triangle. If we were to take a saw and cut it up into

5:48 three separate angles, ...and then if we were to take those three angles and rearrange them

5:54 so that they’re right next to each other like this,

5:57 you can see that the total would be the same as a straight angle... that’s 180 degrees!

6:04 And this will work no matter what type of triangle it is.

6:07 Knowing that a triangle’s angles will always add up to 180 degrees can

6:12 really help you out when solving geometry problems.

6:16 There’s a whole lot of situations where you’ll know what two of the angles are,

6:20 but you need to figure out what the third angle is. Like in this problem.

6:25 With this triangle, we’re told that one of the angles is 35 degrees,

6:29 and the other is 45 degrees. But the third angle is unknown. We need to figure out what it is.

6:37 Since we know that the total must be 180 degrees,

6:40 we can just add up the angles that we DO know,

6:43 and then subtract that from 180 degrees to see what’s left over.

6:48 The leftover amount MUST be the measurement of the unknown angle.

6:53 So, 35 + 45 = 80 degrees.

6:58 And when we take that 80 and subtract it from 180

7:01 we get 100 degrees left over.

7:04 That means that our unknown angle is 100 degrees!

7:07 And, you can always check your answer by adding up all the angles to make sure you get 180.

7:15 So you can see why it’s so important to know that a triangle’s angles add up to 180 degrees!

7:21 Well, that’s all we’re going to learn about triangle is this video.

7:25 Remember, the key to really learning math is to do it.

7:28 So, be sure to practice by doing the exercises for this section.

7:32 As always, thanks for watching Math Antics!

7:34 and I’ll see you next time!

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