Understand Quadrilaterals - Trapezoid, Rhombus, Parallelogram, Rectangle, Square, Kite - [13]

hello welcome back the title of this lesson is understanding and classifying quadrilaterals uh this is part one so quadrilateral it has a very scary sounding name quadrilateral is a simple concept it just means a four-sided figure a figure that forms a closed shape that has only four sides not five sides not three sides remember three sides is a triangle well anything that makes a four-sided figure we call a quadrilateral now we have lots of different kinds of quadrilaterals we're going to go through them several times i have some slides here and we're going to go through them a few times so you'll understand what they are and then we're going to solve a few problems so that you understand what the different quadrilaterals really mean and how to practice that so here we go we're going to go through them fast the first time then we're going to start back over and talk a little more and for now i want you to ignore all of this colored text don't even look at it because i don't want you to focus on that in the beginning i want to go through it and get the big picture and then we'll cycle through it again and talk about these details all right we have a parallelogram you can think of it as a slanted rectangle it looks like a rectangle right but it's slanted so we're going to go through the the details in a second but that is what a parallelogram is next we have a rhombus it looks really similar but you can think of a rhombus as a slanted square remember a square is a figure that has four equal sides right and there's some other things that we'll talk about in a second when we get to square but a rhombus is a slanted square so you can think of it that way so we have a slanted rectangle we have a slanted square now we get to the concept of a rectangle we're not going to get into the details here we're going to talk about that in just a second but you can see two of the sides are parallel these two sides are parallel but a rectangle has four right angles and when you see four right angles you know that the shape is not slanted because if it's slanted like here these angles cannot be 90 degrees perpendicular like that so that's why there are no squares in the corner over here but for rectangles we know that we have four right angles essentially that's that's what a rectangle is then we have a square which is a type of rectangle that has the same sort of thing four right angles but it also has equal sides a square has to have equal sides and four right angles that's why i told you that a rhombus is like a slanted square because a rhombus has to it has to have four equal sides as well but the 90 degree angles are not there that just means it's slanted and then we said a rectangle here had uh the four ninety degree right angles and then we compared that with a parallelogram a slanted rectangle a similar sort of deal but we don't have these right angles again we're going to cycle through them a little bit more detail in a second we're just getting the big picture lastly we have a kite that's four-sided figure as well a kite is a quadrilateral a four-sided figure where two of the adjacent sides that means the sides that are right next to each other are equal these sides are equal and then also these sides are equal we'll get we'll talk more about the kind of the math speak in the bottom but basically a kite has that typical kite shape because these are equal and these are equal all right and then finally we have a trapezoid a trapezoid kind of looks like a rectangle but obviously it's not because we don't have these 90 degree angles and we're going to talk more about that in a minute but a trapezoid has one pair of parallel sides but the other two sides are not not parallel all right so we have the six quadrilateral shapes now we kind of got the big picture now we want to cycle through them again talk about them a little more detail all right back from the top a parallelogram is just a four-sided shape which means a quadrilateral where opposite sides are parallel that's why it's called parallelogram you have to have parallel sides and the opposite sides are parallel that means this side is parallel with this side that means they never intersect if i were to extend these lines and this side is parallel with this side but notice that it doesn't tell me anything about the angles in here so the parallelogram in general can be slanted as much as you want there or it could be straight up and down as well and so any shape that has opposite sides that are parallel like that are is called a parallelogram for a parallelogram opposite sides are parallel and w z which means this line segment is equal to which means the same length as x y and w x this side is the same length as this side z y so when you read through this math you really need to read it and understand what it's saying all this blue stuff is telling me is that this side is equal to this side and this side is equal in length to this side and the other thing is that they have to be opposite sides which are parallel so ultimately in your brain it's going to be a rectangular shape that can be slanted that's all a parallelogram is now these green things are telling you that the angle xwz xwz this angle is the same as this angle xyz so all it's telling you is that this angle is the same as this angle and you can see from the figure that it looked to be about the same and also that this angle here is the same as this angle here so what it's telling you is that in a parallelogram opposite pairs of the sides are parallel and opposite pairs or sides are the same length this means opposite sides are the same length opposite sides are parallel and opposite angles are also parallel okay now keep that in your mind and let's go compare that to what a rectangle is a rectangle is a type of parallelogram how do we know this because it says right here a rectangle is a parallelogram with four right angles because remember a parallelogram means opposite sides have to be parallel okay check this is parallel with this and this is parallel with this a parallelogram opposite sides have to be equal length this side is equal to this one this side is equal to this one check this means opposite angles are equal that's all this green stuff is telling you this angle is equal to this one and this one's equal to this one opposites angles are the same check the only difference between a rectangle and a parallelogram is you have four right angles and that's what makes that rectangular shape up and down and then side to side like this it's perpendicular 90 degree angles in every single corner right now if you read through the math all it's telling you is o l is equal to n m o l is equal to m m it's telling you that this side is equal to this one and this is telling you that this side is equal to this one this is telling you that this angle is equal to this one and this angle is equal to this one it looks like a bunch of math gobbley but if you read through it that's all it's saying angle n-o-l n-o-l is equal to l m o l m right so uh n so all the opposite angles are the same in fact all the angles are the same for a rectangle now let's go back here we talked about parallelogram opposite sides are parallel opposite lengths of the same side are the same size length opposite sides are the same length and also opposite angles are the same so a rhombus is a type of parallelogram that has four equal sides literally it's the same thing as a parallelogram but the sides are equal length that's why it's a slanted square looking thing all this math is telling you down here is that this side is equal to this side and this side is equal to the side in length and this angle is equal to this angle and this angle is equal to this angle that's all that that math is telling you down there and then we can turn our attention to a square because a square is a special case of a rhombus right it's a rectangle with four sides that's true but a rectangle is a parallelogram with four right angles uh here and we know that a square has four equal sides so if we know it's a parallelogram because it tells us right here a rectangle it's a rectangle with four sides and we know a rectangle is a parallelogram but we know it has four sides that's exactly what a rhombus is it's a parallelogram with four equal sides so essentially you have this rhombus thing this parallelogram with four equal sides if you make the angles 90 degrees in the corner you get a square four equal sides of a square four 90 degree right angles so from the top we have this parallelogram it's a slanted rectangle when you make these angles 90 degrees it becomes a rectangle when you take your parallelogram and make all the sides equal you get a rhombus okay when you take a rhombus and give it 90 degree angles in all the corners you get a square because you have equal sides there and then we talked about a kite is just when you have adjacent sides what we call congruent which means they're equal in length this is congruent to this and this one is congruent to this one that's all this is telling you and then you have this trapezoid a trapezoid is when you have two opposite sides parallel that's what this means h i parallel to kj these are parallel but the other sides are not parallel because if they were also parallel it would they would be a parallelogram but since you only have one pair of parallel sides instead of two pairs of parallel sides we call it a trapezoid all right so we've gone through it and now what we want to do is put our problems on the board to practice our skills first problem here is a quadrilateral a four-sided figure we want to first answer what type of quadrilateral is it well we have this side parallel to this side and this side parallel to this side we don't see any 90 degree angles and we know that all four of these sides are not equal that is a parallelogram a parallelogram is a shape where opposite sides are parallel and where two of the sides are equal and the other two parallel sides are also equal that's exactly what we have equal equal and equal equal and parallel parallel and parallel and parallel so we have a parallelogram so instead of writing parallelogram out i'm going to write parallel ram you can write parallelogram a million times if you like i'm just going to write parallelogram there all right next question what line segment is parallel to wz what line segment is parallel to w z here's wz the parallel line segment has to be this one which is x y x y so x y is the line segment that is parallel to w z all right problem number two here we have this quadrilateral this four-sided figure what type of shape is it well we have parallel sides here and parallel sides here that right away in addition to the fact that this looks to be the same length as this one and this one looks to be the same length as this one that looks like it's a parallelogram so you could say that it's a parallelogram which is true this is a parallelogram but it's a special parallelogram it's the type of parallelogram that we actually call a rectangle which is a parallelogram that has four right angles in the corner and that means that the sides of the parallelogram are going to be straight up and down which is what we know a rectangle is so because of that this shape you could put parallelogram but it's more specifically called a rectangle so you can just put rect there and we want to answer the question what is the measure of angle efg e f g that's this angle the measure of this you see the square means it's a 90 degree angle so we know because the shape has a little square in the corner we know it's 90 degrees all right we have this quadrilateral on the board we want to answer what kind of shape is it uh well it looks like a kite and so we know it as a kite but why do we know this it doesn't specifically say on the drawing usually to show that two sides are equal you put a little line through it here and a line through it here that means these sides have equal length and then to show that these are equal length you can mark it with a double line and a double line so the double lines mean those are congruent congruent means equal length in a drawing and these singles go together as being the same length also so the drawing is like this you know that these are the same length and these are the same length it's a quadrilateral where two adjacent sides are the same length and two the other adjacent sides are the same length so you know that that is a kite right because a kite has the definition that it doesn't really say here but it's saying that adjacent sides are equal and the other two adjacent sides are also equal that's what a kite is so this is a kite and then the next question says what line segment is congruent to b c to b c what line segment's congruent has to be this one which is c d this line segment here c d is congruent to b c all right here's our next figure what shape what type of quadrilateral is this well we have a pair of parallel segments here but the other sides are not parallel so this cannot be a parallelogram for parallelogram you have to have opposite sides both pairs of opposite sides to be parallel but these are not parallel only one side is parallel and so because of that we have a special name called a trapezoid trap e zoid trapezoid and if you want to convince yourself of that make sure you understand that a trapezoid just means h i in this drawing h i was parallel to kj this one it means these are parallel doesn't matter what the rest of the figure looks like those have to be parallel when you only have one pair of sides which are parallel it's called a trapezoid now the next question what line segment is parallel to kj kj is this one the one that's parallel to kj is h i so the one that's parallel to kj is h i like this all right the next problem first what type of shape is this well we have parallel parallel and also parallel parallel and it appears that the length of this is the same as the length of this and the length of this is the same of the length of this we didn't mark it if you wanted to mark and show that you would say this is the same length as this and this one is the same length as this one but more than that they're actually all equal to each other in length it looks like this and this and this and this are all the same so we can mark it we can put the double marks everywhere or just single marks everywhere and that means that all four sides are exactly the same length four sides exactly the same length four 90 degree angles in the corner we call this a square we call it a square and the question is name all segments congruent to lm all segments congruent to lm so it's just going to be all the other ones we have m n which is this one here we have n o which is this one and we have ol which is this one so all of them are congruent to the segment lm because they're all the same length all equal length with each other all right here's our final problem what shape is this well it looks like a square that's tilted on its side and so you should start thinking about rhombus now what is a rhombus really anyway it means that we have a parallelogram where four sides are equal this is parallel with this this is parallel with this and it appears that all four sides are equal even though i didn't really tell you that if i wanted to really tell you that i would just mark a congruency line here these little marks mean all four sides are the same length so you have all four of the same length you have opposite sides are parallel that is what a rhombus is go back to our definitions it's a parallelogram with four equal sides opposite sides are equal opposite angles are also equal and of course it's a parallelogram so this angle is equal to this one and also this angle is equal to this one so we call this a rhombus all right and the final question uh what angle is congruent to angle qts angle qts qts is this angle what angle is congruent to this one it's the opposite angle is congruent we can call it q r s angle q r s q r s this angle is congruent because opposite angles are congruent or equal to each other in a rhombus so we have conquered the idea of quadrilaterals they seem very very confusing at first but then when you start realizing that you have the general shape of a parallelogram and then the other ones are like mostly subsets of that then or special cases of that then it becomes a lot easier to understand so i'd like you to go through this again make sure you understand what the different shapes are make sure you understand how we got the answers to all of these problems that we've done practice them yourself follow me on to part two we'll get a little more practice

Channel: Math and Science

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Keywords: trapezoid, quadrilateral, rhombus, parallelogram, kite, rectangle, square, parallel, angle, classify quadrilaterals, quadrilateral definition, what is a trapezoid, what is a parallelogram, what is a rhombus, rhombus definition, parallelogram definition, trapezoid definition, 90 degree angle, properties of quadrilaterals, properties of rhombus, properties of parallelograms, kite properties, parallelogram properties, properties of rectangles, rectangle properties, rhombus properties, math

Id: s02Jl7LhKwI

Length: 16min 42sec (1002 seconds)

Published: Tue Apr 20 2021