All right, this is [fourth-grade] module for Lesson 16
And we're going to continue talking about quadrilaterals
Basically what this means is okay in the 26 years of my teaching sometimes it drives me crazy
When I ask my students to draw a rhombus and they know what a rhombus is
But their rhombus that they draw is just ugly as all heck and so
we're going to in this lesson reason about the attributes of these basic figures and then use a
Special grid paper to to draw better versions of these things so they [don't] have to look so ugly [now]. Let's get started on this
So I'm going to start off with some triangular paper, and if we're told to draw a rhombus
[I'm] going to be able to I can
Look at this triangular paper
And we want our students to be [able] to just kind of like see a rhombus in in the midst [of] all this grid
Now the idea is a rhombus
has to have four
sides that [are] all the exact same length, and we're supposed to have so it's like a square, but
it's not necessarily going to have 90-degree Angles and
So one way to draw that is to go start
Here, and you'll see okay. What I've done is. I've drawn like a three unit length
piece a three unit length line and
Let's see if I can show [it] one two [three]. So there's my [three] unit length line and so
From here, [I] need to draw another one that is also three units, so I'm going to draw
three units one two
three and then I'm going to complete that on this side one two three and then
Complete it on this side one two three now. I now have my rhombus because I've got all four
sides
Are the same length [I've] got?
this side is
Parallel [with] this side, and I've got this side is parallel with this side
I now have a rhombus
Now if we wanted to draw a rectangle on this same
Triangular paper now. It's going to get a little on the ugly side
Because of [course] a rectangle has to have some 90-degree angles, and I don't see any 90-degree Angles here
So what that's going to [mean] is?
Well, let's say, I'm going to start
Here, and I'll draw one two three four five. So I've drawn a five unit
line
And what I'm going to do is I'm going to grab it. I'm going to grab it here and
let's see if I can grab it and
I'm going to make a copy of it and
Let's see ungroup, and I'm going to click [on] this guy
there we go and
Oops, thanks there, and I'm going to duplicate it
Alright, so now I got this guy [and] so it's the same and I'm going to move it over
And I can move it to right here. I could have stopped here, but I'm going to go right here, and so you notice
[I'm] on the kind of like the
Vertex right here, and now I'm just going to draw against the lines. There are no
Lines to Follow down here. I'm just going to keep going
There I've just created a rectangle on my triangular paper. Nothing fancy students probably could have done this since first grade
[but] the idea is how to use grid paper to assist us in our drawing and of course we've satisfied all the requirements
of a rectangle in this case two parallel two pairs of
Parallel lines, there's one pair and here's another pair and most importantly we've got
four
90-Degree Angles
Now in this case. We've got rectangular grid paper, and we want to draw a parallelogram, so
Parallelogram [alright] now. What is a parallelogram? Well? We know [that] a parallelogram has to have four
Four sides and we need two pairs of parallel lines okay? So what does that mean well?
I'm going to start by drawing
just one single line and in this case it happens to [be]
Four units in length, you can see one two [three] four so it's four units and [what] I'm going to do is
I'm going to
select this guy and
I'm going to
duplicate him
So now I've got this guy now. We know
If I were to stop here, it looks like I'm about to make
A rectangle, but to turn it into a parallelogram watch what happens. I'm going to take this guy
I'm just going to raise him [up] one or two units. It doesn't matter exactly how many units I raised him up two units
now
When I connect my dots my lines
I'm going to go from here to [here] and then here to here. I just [created] a parallelogram
Because what is a parallelogram? [well], it's got to have four sides
Which it does and it's got to have two pairs of Parallel lines
But you don't need to have 90-degree angles and sure enough
I don't have any nine to do very angles here, so I just created a parallelogram [on] this really nice
Grid paper
now if I wanted to create just any old
quadrilateral on my rectangular grid paper
[I] could do that. I can do. Oh just any old quadrilateral so one I could go here
And go [up] three
go here and
Here now. I have a quadrilateral. Just four sides. There's no parallel lines
No sets of parallel lines. So that's called a quadrilateral, and I'm going to write that down here quad
Lateral quadrilateral
but if I wanted to do it like a trapezoid
So it's got two lines that are parallel so one pair of parallel lines, so I'm going to start
by [drawing] a line and
Then I'm going to draw another line
Parallel to that
But not quite as long. It doesn't have to be as long
so now I
Can grab that guy?
Where is it York's?
ungroup
And want to unlock this guy
Unlock now can I grab them?
[alright], so now I'm going [to] take this line that. I've drawn and you can see it's parallel
And I'm just going to put it anywhere. I want now I could stop at any time and
Oh, let's stop. Oh right here, okay, and now I'm going to connect my endpoints boom
boom I now have a
Trapezoid, so this is a
Trapezoid because it only has
one pair of
Parallel lines right here, [and] it has four sides, but only one pair of parallel lines, so that's a quick route
I don't know what idea hint at how to use triangular paper and
rectangular grid paper to draw some of our basic
quadrilaterals
so let's put this into some practice, so it says construct a quadrilateral with only one set of
parallel sides one set well I kind of showed you that just previously so I'm going to draw a
Line and apparently, I'm going to do it in green and then I'm going to draw another
Length Parallel, but not quite as long, and I'll just put it right here, and then when I connect the lines
the vertex Vertices and
Here you can see I have a quadrilateral because there's four sides
But there's only one pair of parallel sides one set of parallel sides and what what shape did I create I?
created in this case a
Trapezoid
Right in this one
We're going to draw quadrilateral
It's got one set of parallel lines, but this time it's got to have two right angles
This is going to get a little tricky and this is going to be fun
let's see so I'm going to start by drawing a line down here of any length and
then I'm going to draw a second line that is parallel to that first black one only a different length all right, so
in this case I'm going to make it shorter and
Now what I'm going [to] do is I'm going to try. I'm going to grab it now it's parallel still
but this time I'm going to move it to the left so that
well, let's see there it is so that
This corner and this corner are right on top of each other and so what have I done [I] have created
Two parallel I mean a two
Right Angles two 90-degree Angles you can see them right here
Here's a right angle and here's a right angle and now I'm going to
connect these two vertices and
So I've got one set of parallel lines boom
Boom there's my one set of parallel lines
I've got two 90-degree angles just like I was supposed to and what shape did I create I?
created a
Trapezoid and
the last slide [for] this video is we're going to
construct a quadrilateral
[we're] going to have two sets of parallel sides
Right and what shape did we create so they didn't give us a lot of criteria?
Just quadrilateral, so it's got to have four sides four
sides
and it's got to have
two sets of parallel [sides]
So we have a bunch of choices here ones two sets of parallel sides so we could
there you can see two sets of parallel sides there's one set of parallel sides and
There's another set of parallel sides so what did we create we just created a rectangle?
But that's not the only answer that could have worked
We could have drawn
Let's see all we could have drawn a parallelogram. We could have said okay. Let's draw
one
three unit length here and
then I could have drawn another three unit length, but slightly raised up a little bit right [here] and
then when I do that and
connect these dots I
Have two sets of parallel lines. There's one
there's a set and
there's a set all right here, but I don't have a rectangle anymore now I have a
parallelogram
But we didn't have to do that now. What could we have done?
[oh], we could have done a rhombus a rhombus would be a little bit trickier to draw on this figure
On this paper, but let's see a rhombus could look like oh, I could start here, and I could go [over] to
Up three and I can go over three up
Up to over [three] up three
[over] two, and then I could go to three one two
And then there is my rhombus, so I could draw a rhombus that looks like that. So I've drawn four
Sides, and they happen to all be equal sides in this case, but now we have
One pair one set of Parallel lines and another set of Parallel lines
So now I've just drawn a rhombus and really if I wanted to be super clear [in] this case. I could say that
All four side lengths are the same
Whereas up here. I could say these two are the same and these two are the same [and]
Similarly I could say that this side [is] equal to this side and this side
Two lines is is the same length as this side so congruent?
So man on this figure. I could have drawn oh geez I could draw square. I could draw square now
I'm going to squeeze that in because it's so easy but boom boom boom there it is
There's a square, and it's a quadrilateral, [and] it's got two sets of parallel sides
here's one set and
here's another set so this question was really ripe, and we could have drawn any one [of] these four figures and
that wraps up
grade [four] module four lesson [sixteen]
Talking about quadrilaterals and reasoning about their attributes