Learn Equilateral, Scalene & Isosceles Triangles and Acute, Obtuse & Right Triangles - [15] - By Math and Science
Transcript
| 00:00 | Hello . Welcome back . The title of this lesson | |
| 00:02 | is called understanding and classifying triangles . Really excited to | |
| 00:07 | teach us because actually , you know , people look | |
| 00:09 | at triangles and think what's the big deal ? It's | |
| 00:11 | just a three sided shape . It's a triangle , | |
| 00:13 | right ? But actually triangles are used like so much | |
| 00:18 | in math . I can't even describe to you how | |
| 00:20 | often triangles are used . I can't get too far | |
| 00:23 | ahead of the discussion but just trust me that even | |
| 00:26 | when you get into college and beyond , you're dealing | |
| 00:29 | with triangles constantly . There's an entire field of math | |
| 00:32 | called trigonometry will be just learn about triangles . So | |
| 00:36 | it's very very important in this lesson . We're going | |
| 00:38 | to classify and understand what the triangle is . First | |
| 00:41 | of all , a triangle , there's two things I | |
| 00:42 | want you to understand about all triangles and here they | |
| 00:44 | are . A triangle is a three sided shape . | |
| 00:47 | That's a closed figure , right ? So you can | |
| 00:50 | have tall skinny triangles , you can have short fat | |
| 00:52 | triangles and so on . But they all have three | |
| 00:55 | sides that form a closed shape . The next important | |
| 00:58 | fact about the triangle . I want you to remember | |
| 01:00 | this until the end of time . The angles that | |
| 01:03 | are inside the triangle in all of the corners . | |
| 01:05 | If you measure those angles For triangles , they always | |
| 01:09 | add up to 180°. . I'll say it again . | |
| 01:13 | Inside of a triangle . All three angles add up | |
| 01:16 | to 180°. . Always for every triangle , no matter | |
| 01:20 | if it's a tall skinny triangle , a short triangle | |
| 01:23 | , lots of different different triangles are going to learn | |
| 01:25 | about Third time . I'll say all of those inside | |
| 01:27 | angles add up to 180°. . It is a fact | |
| 01:30 | of all triangles and I want you to remember it | |
| 01:32 | because you're going to use it For like the next | |
| 01:34 | 20 years of your life . Trust me . When | |
| 01:36 | you go far enough in math , will will use | |
| 01:37 | that fact constantly over and over . All right . | |
| 01:40 | So let's talk about some different kinds of triangles . | |
| 01:43 | The triangle , that's the easiest to understand is called | |
| 01:45 | an equal lateral triangle . Equal lateral . Just means | |
| 01:49 | that all sides are equal . That's basically what it | |
| 01:51 | means . All sides are equal and all angles on | |
| 01:54 | the inside are equal . Now these little marks that | |
| 01:57 | are drawn through the sides . You see there's a | |
| 01:59 | mark here , a mark here and a mark here | |
| 02:01 | . Those mean that the sides with the markings on | |
| 02:04 | them are all congruent When we're drawing shapes and geometry | |
| 02:07 | . We don't say things are really equal . We | |
| 02:09 | say that they are congruent . That means essentially they're | |
| 02:12 | the same length . Right ? In other words , | |
| 02:14 | this line is in a different direction than this line | |
| 02:17 | , so they're not the same line segment , but | |
| 02:19 | they do have the same length . So we call | |
| 02:21 | them congruent . All three sides are congruent , that's | |
| 02:23 | what the markings mean . And all of these angles | |
| 02:26 | are also the same . Now let me ask you | |
| 02:28 | a question . I just told you there's 180° in | |
| 02:32 | every triangle . So if you know that all three | |
| 02:34 | of these must be equal . And you know that | |
| 02:37 | every triangle , this one included has 180°. . When | |
| 02:40 | you add them all up . What is the measure | |
| 02:42 | of each of these angles will measure of each of | |
| 02:44 | these angles is 60°. . L . M N is | |
| 02:48 | L . M N . This angle this angle is | |
| 02:51 | M N . L . This one here and then | |
| 02:53 | this one here . All of all this is saying | |
| 02:54 | in green , is that every one of these angles | |
| 02:56 | are equal to 60 degrees ? Why ? Because six | |
| 02:59 | times three is 18 , so 60 times three must | |
| 03:03 | be 180 . So if you take 180 , you | |
| 03:06 | divide it by three , you get an angle of | |
| 03:08 | 60° right there . Alright , Equilateral triangle . Very | |
| 03:11 | important now we have another kind of triangle called an | |
| 03:14 | isosceles triangle . An isosceles means that you have this | |
| 03:18 | side and this side are congruent means the same length | |
| 03:21 | , but the base here or the third side of | |
| 03:23 | the triangle , no matter if it's the base or | |
| 03:25 | not , the other side of the triangle is not | |
| 03:27 | the same length as the other two . So equal | |
| 03:29 | lateral has all three equal Isosceles just means two sides | |
| 03:33 | are equal or congruent . And because of that two | |
| 03:36 | angles inside of the triangle are equal . What two | |
| 03:39 | angles do you think are equal in this triangle ? | |
| 03:41 | This angle is going to be the same as this | |
| 03:43 | one . Just because of cemetery . You can see | |
| 03:45 | they look to be about the same . This angle | |
| 03:47 | is much , much bigger than this one . So | |
| 03:49 | it is different . So when Isosceles triangle means you | |
| 03:52 | have two sides that are the same length , and | |
| 03:54 | also to angles that are the same on the inside | |
| 03:57 | . But I guarantee you no matter what these angles | |
| 03:59 | are , If you add them up this plus this | |
| 04:02 | , plus this , it will always equal 180°. . | |
| 04:05 | It's always true of every single triangle . Okay . | |
| 04:08 | And that's what this is saying , these two sides | |
| 04:10 | are equal and these two angles are equal . So | |
| 04:12 | we have an equilateral and isosceles triangle . Let's talk | |
| 04:15 | about the third kind of triangle called a scaling triangle | |
| 04:19 | . It means all sides are different lengths and all | |
| 04:22 | angles are also different measures as well . So we | |
| 04:24 | don't have anything equal in a scaling triangle . Now | |
| 04:28 | we have one mark here to marks here and three | |
| 04:31 | marks there . And what that actually means is that | |
| 04:33 | this is a different length than this one , which | |
| 04:35 | is also a different length than this one . That's | |
| 04:37 | what these little marks mean . And because of that | |
| 04:39 | , this angle you could just see , it looks | |
| 04:41 | different than this one , which looks different than that | |
| 04:43 | one as well . But again , I guarantee you | |
| 04:45 | that if I knew what this angle was and I | |
| 04:47 | knew what this one was and I knew what this | |
| 04:49 | one was . If I add them all up , | |
| 04:50 | you're always going to get 180°. . Even though all | |
| 04:53 | these triangles look different . If you add all the | |
| 04:55 | angles up inside , they always equal 180°. . I | |
| 04:59 | keep saying it because it's something you're going to use | |
| 05:01 | forever in physics in way advanced and calculus , all | |
| 05:05 | kinds of things . We use these facts of triangles | |
| 05:08 | . So when we're talking about how to classify triangles | |
| 05:11 | on their sides , we have equilateral triangle . All | |
| 05:13 | sides equal all angles equal , we have isosceles triangle | |
| 05:17 | , two sides are equal , two angles are equal | |
| 05:19 | and we have the scaling which means nothing is equal | |
| 05:21 | , no sides , no angles , they're all different | |
| 05:24 | . Now if we want to talk about how to | |
| 05:25 | classify these in terms of their angles , we have | |
| 05:28 | other names as well . Okay with the other names | |
| 05:30 | , were all about the sides of the triangle . | |
| 05:32 | Mostly here let's talk about the angles we have , | |
| 05:35 | what we call an acute triangle . If all of | |
| 05:39 | the angles on the inside are acute , which means | |
| 05:42 | acute an acute angle . Remember means less than 90°. | |
| 05:46 | . So if you think of a 90° angle being | |
| 05:48 | straight up and down like this , then this angle | |
| 05:50 | is acute because it's less than 90 . This angle | |
| 05:53 | is acute because it's less than 90 . This angle | |
| 05:55 | is also a cute because it's less than 90 . | |
| 05:57 | If all angles are less than 90 , we call | |
| 06:00 | it an acute triangle , Right , we call it | |
| 06:02 | an acute triangle , all three angles less than 90 | |
| 06:04 | . All three angles are acute . Now here we | |
| 06:08 | have another kind of triangle called a right triangle , | |
| 06:11 | it has one right angle . This little symbol in | |
| 06:13 | the corner means what 90°. . We've used that symbol | |
| 06:16 | before right triangle . I can't even tell you how | |
| 06:19 | important it is . I'm being very serious when I | |
| 06:22 | say we have an entire course called trigonometry that It's | |
| 06:26 | basically learning how to use right triangles . Mostly all | |
| 06:29 | triangles really . But right triangles especially are incredibly important | |
| 06:33 | . I can't tell you exactly how important right now | |
| 06:36 | , but just trust me you're never gonna stop learning | |
| 06:38 | about right triangles . They're very , very important . | |
| 06:40 | A right triangle is just a triangle where one of | |
| 06:42 | the angles is 90° And then we have the obtuse | |
| 06:46 | triangle , which means one of the angles is bigger | |
| 06:49 | than 90°. . So you can think of the obtuse | |
| 06:51 | triangle as the laid back triangle because you have one | |
| 06:54 | angle here , a 90° angle would be right up | |
| 06:56 | and down here . But this one's bigger than that | |
| 06:59 | , which means it's an obtuse angle in here , | |
| 07:01 | which means it's kind of a laid back triangle . | |
| 07:03 | So one more time for the top . In terms | |
| 07:05 | of their angles , we have acute triangles when all | |
| 07:09 | of the angles are less than 90 degrees . We | |
| 07:12 | have right triangles when we have 1 90 degree angle | |
| 07:15 | in there . And we have obtuse triangles when we | |
| 07:18 | have uh one of the angles greater than 90 degrees | |
| 07:21 | the laid back triangle . Now you can also have | |
| 07:24 | a cute isosceles triangles and so on . We can | |
| 07:27 | put the names together . So what I need to | |
| 07:29 | do now is start putting our problems on the board | |
| 07:31 | will get a little practice classifying triangles . Alright problem | |
| 07:36 | number one , we have a triangle here and we | |
| 07:38 | want to ask ourselves what type of triangle is it | |
| 07:40 | ? And we want to use as many descriptors as | |
| 07:43 | possible . We want to use the classifying by the | |
| 07:46 | sides and also classifying by the angles . So what | |
| 07:49 | do we have ? We know that this side is | |
| 07:51 | the same length as this side , that's what the | |
| 07:52 | market is , but this side is a different length | |
| 07:55 | than that , right ? So because we have two | |
| 07:58 | equal sides then we know that it is going to | |
| 08:02 | be an isosceles triangle which is down here . We | |
| 08:04 | know it cannot be equal lateral because equal lateral would | |
| 08:07 | have all three sides be the same , but we | |
| 08:10 | don't have all three sides . We actually only have | |
| 08:12 | two sides . So we know it's going to be | |
| 08:14 | an isosceles triangle , But we also know that this | |
| 08:17 | is an acute angle and this is an acute angle | |
| 08:20 | and this is an acute angle . And remember a | |
| 08:22 | triangle that is an acute triangle has all angles less | |
| 08:26 | than 90°. . All of these angles are less than | |
| 08:29 | 90°. . So what do we call this thing ? | |
| 08:30 | We call it acute , we call it acute isosceles | |
| 08:36 | Yes , I saw sales . So we could just | |
| 08:42 | call it an Isosceles triangle . We could just call | |
| 08:45 | it an acute triangle but we put them both together | |
| 08:47 | because both of them apply , it's an acute isosceles | |
| 08:50 | triangle . Next question name all of these angles here | |
| 08:54 | . We're just getting practice with naming angles . So | |
| 08:55 | we're going to name them here . And so we | |
| 08:57 | have the angles listed as uh X Y . Z | |
| 09:02 | . That's this angle X , Y . Z . | |
| 09:05 | Right . And then we have the angle Y . | |
| 09:08 | Z X , Y , Z . X . That's | |
| 09:12 | this angle right here . And then we have the | |
| 09:15 | angle Z . X , Y . Z . X | |
| 09:20 | . Y . That's this angle . So the first | |
| 09:21 | one goes with this one , this one goes with | |
| 09:23 | this one and this one goes with this one , | |
| 09:25 | notice the middle part is the vertex of each of | |
| 09:28 | the angles , the pointy part of each of the | |
| 09:30 | angles . Alright problem number two we have this triangle | |
| 09:33 | and we want to first write down the type of | |
| 09:35 | this triangle . Well we see immediately that we have | |
| 09:38 | a right angle here and if we have one right | |
| 09:40 | angle we learned a minute ago that means this is | |
| 09:42 | a right triangle . But we also know that this | |
| 09:45 | side is the same length as this one , but | |
| 09:47 | this side is different . So it's only two of | |
| 09:49 | the sides that are equal . So because two of | |
| 09:51 | the sides are equal , that's called isosceles , remember | |
| 09:54 | . And because it has a right angle , that's | |
| 09:56 | called a right triangle . So we're going to call | |
| 09:58 | this an isosceles right triangle or you could call it | |
| 10:01 | a right isosceles , you could call it a right | |
| 10:11 | isosceles triangle . All right . For the next part | |
| 10:13 | of the problem , let's find the measure of angle | |
| 10:15 | E g f , E g F . That's this | |
| 10:18 | angle right here , the symbol tells me that that | |
| 10:21 | is a 90 degree angle , 90 degree angle . | |
| 10:25 | All right . Here's problem , number three we have | |
| 10:27 | a triangle . What type of triangle is this ? | |
| 10:29 | Let's take a look . Well , first of all | |
| 10:30 | , we see it's a laid back triangle . This | |
| 10:32 | angle , If it were straight up and down would | |
| 10:34 | be 90°. . But it's larger than that . So | |
| 10:37 | because it is one of these angles is larger than | |
| 10:40 | 90°. . This is an obtuse triangle right up to | |
| 10:44 | us . So we know it's an obtuse triangle . | |
| 10:47 | And it's also a what kind scaling triangle ? Why | |
| 10:51 | is that ? Because uh we have three different lengths | |
| 10:55 | . Right . So remember , a scallion is when | |
| 10:58 | all of the three lengths are totally different . So | |
| 11:00 | it's an obtuse triangle . It's also a scaling triangle | |
| 11:03 | . So we put those guys together , we call | |
| 11:04 | it obtuse scaling . All right . Up to scaling | |
| 11:12 | triangle . Alright . Question which angle is greater than | |
| 11:15 | 90 degrees . We just said it was this one | |
| 11:17 | . So we're going to name an angle abc angle | |
| 11:21 | A . B . C . And that's the final | |
| 11:25 | answer . All right . Here's problem No four . | |
| 11:27 | What kind of triangle is this ? Well , this | |
| 11:29 | side is the same length as this side . Also | |
| 11:32 | the same length as that . So we know it's | |
| 11:35 | an equilateral triangle . We also know these . All | |
| 11:38 | three of these angles are acute angle . So if | |
| 11:40 | we want to be totally correct , we will call | |
| 11:42 | it acute equal lateral . Yes equal at all . | |
| 11:52 | Let me just double check the spelling on equal . | |
| 11:54 | Electoral . That's right . Okay , acute equilateral . | |
| 11:57 | All right . Next question , what is the measure | |
| 12:00 | of angle H J I H j Ai That's this | |
| 12:03 | angle measure right there . And you might say , | |
| 12:05 | well we never we never told that . Well actually | |
| 12:08 | we were told that Uh in the beginning , but | |
| 12:10 | we also figured it out ourselves because we know all | |
| 12:12 | triangles have to have 180°. . And since this is | |
| 12:17 | equal lateral , all three of these are equal . | |
| 12:18 | So if you take 180 and you divide it by | |
| 12:21 | three . Think of 18 divided by three , that's | |
| 12:23 | six . So 180 divided by three is 60 . | |
| 12:28 | And we actually said that here that all of these | |
| 12:30 | angles for an equilateral war equal to 60°. . So | |
| 12:33 | we know this angle is equal to 60° as well | |
| 12:37 | , just like this one , this is 60 and | |
| 12:38 | this one's also 60 as well . Yeah . Alright | |
| 12:41 | problem No five . What type of triangle do we | |
| 12:43 | have here ? This is different than this which is | |
| 12:46 | different than this . That means it's a scaling triangle | |
| 12:49 | . Also this is an acute angle , this is | |
| 12:51 | an acute angle , this is an acute angle , | |
| 12:53 | it's an acute triangle . So together they're called acute | |
| 12:57 | scaling acute scaling triangle , question name all of the | |
| 13:04 | sides of this triangle , all of the line segments | |
| 13:06 | that make the side . So we could call this | |
| 13:08 | L . M . That would be this side here | |
| 13:12 | . And we could call it M . N . | |
| 13:14 | Which would be this side right here . And then | |
| 13:17 | we could call it N . L . Which is | |
| 13:19 | this side right here . Just getting a little practice | |
| 13:21 | with writing the names of line segments . Alright problem | |
| 13:25 | six . What kind of triangle do we have here | |
| 13:27 | ? Well we see right away . This is an | |
| 13:29 | acute angle . This is an acute angle but this | |
| 13:31 | one this would be a right angle , it's larger | |
| 13:34 | than that . This is an obtuse angle . So | |
| 13:37 | because of that it's obtuse triangle so we'll put obtuse | |
| 13:40 | right . But we can also realize that this is | |
| 13:45 | a uh isosceles triangle because these two sides are equal | |
| 13:49 | but the third one is different . Remember isosceles means | |
| 13:51 | you have two equal sides , so it's an obtuse | |
| 13:55 | isosceles triangle , obtuse isosceles triangle question . Name the | |
| 14:04 | angles that measure less than 90 degrees . Well we | |
| 14:07 | just said this one's bigger than 90 and this one's | |
| 14:10 | way less than 90 and this one's way less than | |
| 14:12 | 90 . So it's these two angles . So let's | |
| 14:14 | name them . How can we name them ? R | |
| 14:17 | . S . Q . Would be this one R | |
| 14:19 | . S . Q . And then this one over | |
| 14:22 | here is our Q . S . R . Q | |
| 14:27 | . S . R . Q . S . Is | |
| 14:29 | this one ? R . S . Q . Is | |
| 14:32 | this one ? So in this lesson we have learned | |
| 14:34 | how to classify triangles . And I mean it when | |
| 14:36 | I say triangles are used so much in math in | |
| 14:39 | real life too . And so we're learning how to | |
| 14:41 | classify triangles based on their size , I'm sorry , | |
| 14:44 | their sides which would be uh you know if it's | |
| 14:47 | an equilateral triangle or an isosceles triangle or a scaling | |
| 14:51 | triangle . And we also can classify triangles based on | |
| 14:54 | their angle . Is it an acute triangle where all | |
| 14:57 | the sides are less than 90 ? Is it an | |
| 14:59 | obtuse triangle where one of the angles is larger than | |
| 15:02 | 90 ? Or is it that really special triangle ? | |
| 15:04 | The right triangle that has a 90° angle ? The | |
| 15:07 | right triangle especially important is going to be used throughout | |
| 15:10 | math . You'll learn so much about that as we | |
| 15:12 | go farther . So I'd like you to rewind this | |
| 15:15 | , Make sure you get all of these correct , | |
| 15:16 | Make sure you understand all of the differences that we | |
| 15:18 | talked about here . Follow me on the part two | |
| 15:20 | , we'll get a little more practice . |
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