Understand Quadrilaterals - Trapezoid, Rhombus, Parallelogram, Rectangle, Square, Kite - [13] - By Math and Science
Transcript
| 00:00 | Hello . Welcome back . The title of this lesson | |
| 00:02 | is understanding and classifying quadra laterals . This is part | |
| 00:06 | one . So quadrille lateral , it has a very | |
| 00:09 | scary sounding name . Quadrilateral is a simple concept . | |
| 00:12 | It just means a four sided figure . A figure | |
| 00:15 | that forms a closed shape that has only four sides | |
| 00:18 | , not five sides , not three sides . Remember | |
| 00:21 | three sides as a triangle . Will anything that makes | |
| 00:24 | a four sided figure , we call a quadrilateral . | |
| 00:26 | Now we have lots of different kinds of quadrilateral . | |
| 00:28 | We're going to go through them several times , have | |
| 00:31 | some slides here and we're gonna go through them a | |
| 00:32 | few times . You understand what they are and then | |
| 00:35 | we're gonna solve a few problems so that you understand | |
| 00:37 | what the different quadrilateral is really mean and how to | |
| 00:39 | practice that . So here we go . We're gonna | |
| 00:41 | go through them fast the first time that we're going | |
| 00:43 | to start back over and talk a little more . | |
| 00:45 | And for now I want you to ignore all of | |
| 00:48 | this colored text . Don't even look at it because | |
| 00:50 | I don't want you to focus on that in the | |
| 00:52 | beginning . I want to go through it and get | |
| 00:53 | the big picture and then we'll cycle through it again | |
| 00:55 | and talk about these details . All right . We | |
| 00:58 | have a parallelogram . You can think of it as | |
| 01:01 | a slanted rectangle . It looks like a rectangle , | |
| 01:03 | right ? But it's slanted . So we're gonna go | |
| 01:06 | through the the details in a second . But that | |
| 01:08 | is what a parallelogram is . Next . We have | |
| 01:11 | a rhombus . It looks really similar , but you | |
| 01:13 | can think of a rhombus as a slanted square . | |
| 01:16 | Remember a square is a figure that has four equal | |
| 01:19 | sides , Right ? And there's some other things that | |
| 01:21 | we'll talk about in a second when we get to | |
| 01:23 | square . But a rhombus is a slanted square . | |
| 01:26 | So you can think of it that way . So | |
| 01:27 | we have a slanted rectangle . We have a slanted | |
| 01:29 | square . Now we get to the concept of a | |
| 01:32 | rectangle . Uh we're not going to get into the | |
| 01:34 | details here , we're gonna talk about that in just | |
| 01:36 | a second , but you can see two of the | |
| 01:37 | sides are parallel . These two sides are parallel , | |
| 01:40 | but a rectangle has four right angles . And when | |
| 01:43 | you see four right angles , you know that the | |
| 01:46 | shape is not slanted because if it's slanted like here | |
| 01:50 | , these angles cannot be 90 degrees perpendicular like that | |
| 01:53 | . So that's why there are no squares in the | |
| 01:55 | corner over here . But for rectangles we know that | |
| 01:58 | we have four right angles essentially . That's that's what | |
| 02:00 | a rectangle is . Then we have a square which | |
| 02:03 | is a type of rectangle that has the same sort | |
| 02:07 | of thing . Four right angles , but it also | |
| 02:10 | has equal sides . A square has to have equal | |
| 02:12 | sides and for right angles . That's why I told | |
| 02:15 | you that a rhombus is like a slanted square because | |
| 02:19 | a rhombus has to it has to have four equal | |
| 02:21 | sides as well . But the 90 degree angles are | |
| 02:24 | not there . That just means it's slanted . And | |
| 02:27 | then we said a rectangle here had the 4 90 | |
| 02:30 | degree right angles . And then we compared that with | |
| 02:33 | a parallelogram . A slanted rectangle , similar sort of | |
| 02:37 | deal . But we don't have these right angles . | |
| 02:39 | Again , we're gonna cycle through them a little bit | |
| 02:41 | more detail on the second . We're just getting the | |
| 02:42 | big picture . Lastly we have a kite that's four | |
| 02:45 | sided figure as well . A kite is a quadrille | |
| 02:49 | lateral a four sided figure where two of the adjacent | |
| 02:53 | sides , that means the sides that are right next | |
| 02:55 | to each other are equal . These sides are equal | |
| 02:58 | and then also these sides are equal . We'll get | |
| 03:01 | we'll talk more about the kind of the math speaking | |
| 03:03 | the bottom . But basically a kite has that typical | |
| 03:06 | kite shape because these are equal and these are equal | |
| 03:08 | . All right . And then finally we have a | |
| 03:10 | trapezoid . A trapezoid kind of looks like a rectangle | |
| 03:13 | . But obviously it's not because we don't have these | |
| 03:15 | 90° angles . And we're gonna talk more about that | |
| 03:18 | in a minute . But trapezoid has one pair of | |
| 03:21 | parallel sides but the other two sides are not not | |
| 03:25 | parallel . All right . So we have the six | |
| 03:28 | quadrilateral shapes . Now we kind of got the big | |
| 03:30 | picture . Now we want to cycle through them again | |
| 03:33 | . Talk about them a little more detail . All | |
| 03:35 | right back from the top . A parallelogram is just | |
| 03:38 | a four sided shape , which means a quadrilateral where | |
| 03:41 | opposite sides are parallel . That's why it's called parallelogram | |
| 03:46 | . You have to have parallel sides and the opposite | |
| 03:48 | sides are parallel . That means this side is parallel | |
| 03:51 | with the side . That means they never intersect if | |
| 03:53 | I were to extend these lines and this side is | |
| 03:57 | parallel with this side . But notice that it doesn't | |
| 03:59 | tell me anything about the angles in here . So | |
| 04:02 | the parallelogram in general can be slanted as much as | |
| 04:05 | you want uh there or it could be straight up | |
| 04:08 | and down as well . And so uh any shape | |
| 04:11 | that has opposite sides of your parallel like that are | |
| 04:14 | is called a parallelogram . For a parallelogram , opposite | |
| 04:18 | sides are parallel and W . Z . Which means | |
| 04:21 | this line segment is equal to which means the same | |
| 04:23 | length as X . Y . And W . X | |
| 04:27 | . This side is the same length as this side | |
| 04:30 | , Z . Y . So when you read through | |
| 04:31 | this math you really need to read and understand what | |
| 04:33 | it's saying . All this blue stuff is telling me | |
| 04:36 | is that this side is equal to this side and | |
| 04:38 | this side is equal in length to this side . | |
| 04:41 | And the other thing is that they have to be | |
| 04:43 | opposite sides which are parallel . So ultimately in your | |
| 04:46 | brain it's going to be a rectangular shape that can | |
| 04:49 | be slanted . That's all a parallelogram is . Now | |
| 04:53 | these green things are telling you that the angle X | |
| 04:56 | . W . Z , X W . Z . | |
| 04:58 | This angle is the same as this angle X . | |
| 05:02 | Y . Z . So all it's telling you is | |
| 05:04 | that this angle is the same as this angle and | |
| 05:06 | you can see from the figure that it looked to | |
| 05:08 | be about the same . And also that this angle | |
| 05:11 | here is the same as this angle here . So | |
| 05:13 | what it's telling you is that in a parallelogram , | |
| 05:16 | opposite pairs of the sides are parallel and opposite pairs | |
| 05:20 | or sides are the same length . This means opposite | |
| 05:23 | sides of the same length , opposite sides are parallel | |
| 05:26 | and opposite angles are also parallel . Okay now keep | |
| 05:30 | that in your mind and let's go compare that to | |
| 05:32 | what a rectangle is . A rectangle is a type | |
| 05:37 | of parallelogram . How do we know this ? Because | |
| 05:40 | it says right here . A rectangle is a parallelogram | |
| 05:42 | with four right angles because remember a parallelogram means opposite | |
| 05:46 | sides have to be parallel . Okay , check this | |
| 05:49 | is parallel with this and this is parallel with this | |
| 05:52 | . A parallelogram , opposite sides have to be equal | |
| 05:55 | length . This sides equal to this one . This | |
| 05:57 | one is equal to this one . Check this means | |
| 06:00 | opposite angles are equal . That's all this green stuff | |
| 06:03 | is telling you this angle is equal to this one | |
| 06:05 | and this one is equal to this one . Opposite | |
| 06:07 | angles are the same . Check , the only difference | |
| 06:10 | between a rectangle in a parallelogram is you have four | |
| 06:13 | right angles and that's what makes that rectangular shape up | |
| 06:16 | and down and then side to side like this . | |
| 06:19 | It's perpendicular , 90 degree angles in every single corner | |
| 06:22 | . Right now , if you read through the math | |
| 06:24 | all it's telling you is O . L . Is | |
| 06:26 | equal to N M O L is equal to M | |
| 06:28 | . And it's telling you that this side is equal | |
| 06:30 | to this one and this is telling you that this | |
| 06:32 | side is equal to this one . This is telling | |
| 06:34 | you that this angle is equal to this one and | |
| 06:36 | this angle is equal to this one . It looks | |
| 06:38 | like a bunch of math gobbledygook . But if you | |
| 06:41 | read through it , that's all it sang angle N | |
| 06:43 | O L N O L is equal to O L | |
| 06:46 | M O L M . Right ? So , so | |
| 06:51 | all the opposite angles are the same . In fact | |
| 06:53 | , all the angles are the same for a rectangle | |
| 06:55 | . Now , let's go back here . We talked | |
| 06:57 | about parallelogram , opposite sides are parallel , opposite lengths | |
| 07:01 | of the same side of the same length , opposite | |
| 07:04 | sides of the same length , and also opposite angles | |
| 07:07 | are the same . So a rhombus is a type | |
| 07:09 | of parallelogram that has four equal sides , literally , | |
| 07:13 | it's the same thing as a parallelogram , but the | |
| 07:15 | sides of equal length , that's why it's a slanted | |
| 07:18 | square looking thing . All this math is telling you | |
| 07:20 | down here is that this side is equal to this | |
| 07:23 | side and this side is equal to the side in | |
| 07:25 | length and this angle is equal to this angle and | |
| 07:28 | this angle is equal to this angle . That's all | |
| 07:30 | that . That math is telling you down there and | |
| 07:33 | then we can turn our attention to a square because | |
| 07:35 | a square is a special case of a rhombus right | |
| 07:39 | ? It's a rectangle with four sides . That's true | |
| 07:41 | . But a rectangle is a parallelogram with four right | |
| 07:44 | angles . Uh Here and we know that a square | |
| 07:47 | has four equal sides . So if we know it's | |
| 07:51 | a parallelogram because it tells us right here , a | |
| 07:53 | rectangle , a rectangle with four sides . And we | |
| 07:55 | know a rectangle is a parallelogram but we know it | |
| 07:58 | has four sides . That's exactly what a rhombus is | |
| 08:01 | . It's a parallelogram with four equal sides . So | |
| 08:03 | essentially you have this rhombus thing , this parallelogram with | |
| 08:06 | four equal sides . If you make the angles 90° | |
| 08:09 | in the corner , you get a square , four | |
| 08:11 | equal sides of a square for 90° right angles . | |
| 08:16 | So from the top we have this parallelogram , it's | |
| 08:18 | a slanted rectangle . When you make these angles 90°, | |
| 08:21 | , it becomes a rectangle . When you take your | |
| 08:24 | parallelogram and make all the sides equal , you get | |
| 08:26 | a rhombus . Okay , when you take a rhombus | |
| 08:29 | and give it 90° angles and all the corners you | |
| 08:32 | get a square because you have equal sides there . | |
| 08:35 | And then we talked about a kite is just when | |
| 08:40 | you have adjacent sides . What we call congruent , | |
| 08:43 | which means they're equal in length . This is congruent | |
| 08:47 | to this and this one is congruent to this one | |
| 08:49 | . That's all this is telling you . And then | |
| 08:51 | you have this trapezoid . A trapezoid is when you | |
| 08:53 | have two opposite sides parallel . That's what this means | |
| 08:56 | . H I parallel to KJ . These are parallel | |
| 08:59 | but the other sides are not parallel because if they | |
| 09:02 | were also parallel , it would it would be a | |
| 09:04 | parallelogram . But since you don't have one pair of | |
| 09:07 | parallel sides instead of two pairs of parallel sides , | |
| 09:10 | we call it a trapezoid . All right . So | |
| 09:13 | we've gone through it and now what we want to | |
| 09:15 | do is put our problems on the board to practice | |
| 09:17 | our skills . First problem here is a quadrilateral , | |
| 09:22 | a four sided figure . We want to first answer | |
| 09:24 | what type of quadrilateral is it ? Well , we | |
| 09:27 | have this side parallel to this side and this side | |
| 09:30 | parallel to this side . We don't see any 90° | |
| 09:32 | angles . And we know that all four of these | |
| 09:34 | sides are not equal . That is a parallelogram . | |
| 09:37 | A parallelogram is a shape where opposite sides are parallel | |
| 09:41 | and where two of the sides are equal and the | |
| 09:44 | other two parallel sides are also equal . That's exactly | |
| 09:47 | what we have . Equal . Equal and equal . | |
| 09:49 | Equal and parallel , parallel and parallel and parallel . | |
| 09:53 | So we have a parallelogram . So instead of writing | |
| 09:56 | parallelogram out , I'm gonna write parallel graham . You | |
| 10:00 | can write parallelogram a million times if you like . | |
| 10:03 | I'm just gonna write parallelogram there . All right next | |
| 10:06 | question uh What line segment is parallel to W . | |
| 10:10 | Z ? What line segment is parallel to W . | |
| 10:13 | Z . Here's W . Z . The parallel line | |
| 10:16 | segment has to be this one which is X . | |
| 10:17 | Y . X . Y . So X . Y | |
| 10:20 | . Is the line segment that is parallel to W | |
| 10:22 | . Z . Alright problem No two . Here we | |
| 10:25 | have this quadrilateral is four sided figure . What type | |
| 10:28 | of shape is it ? Well we have parallel sides | |
| 10:32 | here and parallel sides here that right away . In | |
| 10:35 | addition to the fact that this looks to be the | |
| 10:37 | same length as this one and this one looks to | |
| 10:39 | be the same length as this one that looks like | |
| 10:41 | it's a parallelogram . So you could say that it's | |
| 10:44 | a parallelogram which is true . This is a parallelogram | |
| 10:47 | but it's a special parallelogram . It's the type of | |
| 10:50 | parallelogram that we actually call a rectangle , which is | |
| 10:53 | a parallelogram that has four right angles in the corner | |
| 10:55 | . And that means that the sides of the parallelogram | |
| 10:58 | are going to be straight up and down , which | |
| 11:00 | is what we know A rectangle is . So because | |
| 11:02 | of that , this shape you could put parallelogram , | |
| 11:04 | but it's more specifically called a rectangle . So you | |
| 11:08 | just put wrecked there . And we want to answer | |
| 11:10 | the question , what is the measure of angle ? | |
| 11:12 | E f g e FG . That's this angle . | |
| 11:16 | The measure of this , you see the square means | |
| 11:18 | it's a 90° angle . So , we know because | |
| 11:20 | the Shape has a little square in the corner . | |
| 11:23 | We know it's 90°. . All right . We have | |
| 11:27 | this quadrilateral on the board . You want to answer | |
| 11:29 | ? What kind of shape is it ? Uh Well | |
| 11:31 | , it looks like a kite and so we know | |
| 11:33 | it is a kite . But why do we know | |
| 11:35 | this ? It doesn't specifically say on the drawing . | |
| 11:38 | Usually to show that two sides are equal . You | |
| 11:40 | put a little line through it here and little line | |
| 11:42 | through it here . That means these sides have equal | |
| 11:44 | length . And then to show that these are equal | |
| 11:47 | length , you can mark it with a double line | |
| 11:49 | and a double line . So the double lines mean | |
| 11:51 | those are congruent . Congruent means equal length in a | |
| 11:54 | drawing and these singles go together as being the same | |
| 11:58 | length also . So the drawing is like this , | |
| 12:00 | you know that these are the same length and these | |
| 12:02 | are the same length . It's a quadrilateral where two | |
| 12:04 | adjacent sides are the same length and to the other | |
| 12:08 | adjacent sides of the same length . So , you | |
| 12:10 | know that that is a kite , right ? Because | |
| 12:14 | a kite has the definition Mhm . That it doesn't | |
| 12:19 | really say here , but it's saying that adjacent sides | |
| 12:21 | are equal and the other two adjacent sides are also | |
| 12:23 | equal . That's what a kite is . So this | |
| 12:26 | is a kite . And then the next question says | |
| 12:28 | what line segment is congruent to B . C . | |
| 12:32 | To B . C . What line segments congruent has | |
| 12:34 | to be this one which is C . D . | |
| 12:38 | This line segment here , C . D . Is | |
| 12:40 | congruent to B . C . All right . Here's | |
| 12:42 | our next figure . What shape , what type of | |
| 12:45 | quadrilateral is this ? Well , we have a pair | |
| 12:47 | of parallel segments here but the other sides are not | |
| 12:51 | parallel . So this cannot be a parallelogram . For | |
| 12:54 | parallelogram you have to have opposite sides , both pairs | |
| 12:56 | of opposite sides to be parallel , but these are | |
| 12:59 | not parallel . Only one side is parallel . And | |
| 13:02 | so because of that we have a special name called | |
| 13:04 | the trapezoid trap . E . Z . Oid trapezoid | |
| 13:10 | and if you want to convince yourself of that , | |
| 13:11 | make sure you understand that . A trapezoid just means | |
| 13:15 | H . I . In this joint h I was | |
| 13:16 | parallel to KJ . This one it means these are | |
| 13:19 | parallel . Doesn't matter what the rest of the figure | |
| 13:22 | looks like . Those have to be parallel and you | |
| 13:24 | only have one pair of sides which are parallel . | |
| 13:27 | It's called a trapezoid . Now the next question what | |
| 13:30 | line segment is parallel to KJ ? KJ Is this | |
| 13:34 | one the one that's parallel to KJ is H . | |
| 13:37 | I . So the one that's parallel to KJ is | |
| 13:40 | H . I like this . Alright . The next | |
| 13:45 | problem first . What type of shape is this ? | |
| 13:47 | Well we have parallel , parallel and also parallel , | |
| 13:50 | parallel and it appears that the length of this is | |
| 13:53 | the same as the length of this and the length | |
| 13:55 | of this is the same as the length of this | |
| 13:56 | . We didn't market if you wanted to mark and | |
| 13:59 | show that you would say this is the same length | |
| 14:01 | as this and this one is the same length as | |
| 14:04 | this one . But more than that they're actually all | |
| 14:07 | equal to each other in length . It looks like | |
| 14:09 | this and this and this and this are all the | |
| 14:11 | same . So we can market we can put the | |
| 14:14 | double marks everywhere or just single marks everywhere . And | |
| 14:16 | that means that all four sides are exactly the same | |
| 14:19 | length . Four sides exactly the same length , 4 | |
| 14:22 | 90° angles in the corner . We call this a | |
| 14:25 | square , we call it a square . And the | |
| 14:29 | question is name all segments congruent to lm all segments | |
| 14:34 | can grow into L . M . So it's just | |
| 14:35 | gonna be all the other ones . We have M | |
| 14:38 | . N . Which is this one here ? We | |
| 14:41 | have N . O . Which is this one And | |
| 14:44 | we have O . L . Which is this one | |
| 14:46 | ? So all of them are congruent two . The | |
| 14:50 | segment Lm because they're all the same length uh all | |
| 14:53 | equal length with each other . All right . Here's | |
| 14:56 | our final problem . What shape is this ? What | |
| 14:58 | it looks like a square that's tilted on its side | |
| 15:01 | . And so you should start thinking about rhombus . | |
| 15:03 | Now what is a rhombus really ? Anyway it means | |
| 15:06 | that we have a parallelogram where four sides are equal | |
| 15:09 | . This is parallel with this , this is parallel | |
| 15:12 | with this and it appears that all four sides are | |
| 15:14 | equal . Even though I didn't really tell you that | |
| 15:16 | if I wanted to really tell you that I would | |
| 15:18 | just mark a congruence the line here . These little | |
| 15:21 | marks mean all four sides of the same length , | |
| 15:23 | so you have all four of the same length , | |
| 15:25 | you have opposite sides are parallel , that is what | |
| 15:28 | a rhombus is . Go back to our definitions , | |
| 15:30 | it's a parallelogram with four equal sides , opposite sides | |
| 15:34 | are equal , opposite angles are also equal . Uh | |
| 15:38 | And of course it's a parallelogram . So this angle | |
| 15:40 | is equal to this one and also this angle is | |
| 15:42 | equal to this one . So we call this a | |
| 15:44 | rhombus alright . And the final question , what angle | |
| 15:51 | is congruent to angle Q . T . S . | |
| 15:53 | Angle Q T . S . Q T . S | |
| 15:56 | . Is this angle ? What angle is congruent to | |
| 15:58 | this one ? It's the opposite angle is congruent , | |
| 16:00 | We can call it Q . R . S angle | |
| 16:03 | Q R S . Q R S . This angle | |
| 16:07 | is congruent because opposite angles are congruent or equal to | |
| 16:10 | each other in a rhombus . So we have conquered | |
| 16:14 | the idea of quadra laterals . They seem very , | |
| 16:16 | very confusing at first , but then when you start | |
| 16:18 | realizing that you have the general shape of a parallelogram | |
| 16:21 | and then the other ones are like mostly subsets of | |
| 16:24 | that then or special cases of that , then it | |
| 16:27 | becomes a lot easier to understand . So I'd like | |
| 16:29 | you to go through this again , make sure you | |
| 16:30 | understand what the different shapes are , make sure you | |
| 16:33 | understand how we got the answers to all of these | |
| 16:35 | problems that we've done . Practice them yourself . Follow | |
| 16:37 | me on the part two , we'll get a little | |
| 16:39 | more practice . |
Summarizer
DESCRIPTION:
Quality Math And Science Videos that feature step-by-step example problems!
OVERVIEW:
Understand Quadrilaterals - Trapezoid, Rhombus, Parallelogram, Rectangle, Square, Kite - [13] is a free educational video by Math and Science.
This page not only allows students and teachers view Understand Quadrilaterals - Trapezoid, Rhombus, Parallelogram, Rectangle, Square, Kite - [13] videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.
GRADES:
STANDARDS:
