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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!
7:36 Learn more at www.mathantic.com
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