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CCSS Math: HSG.GPE.B.4

Classify quadrilateral ABCD. Choose the option that best
suits the quadrilateral. We're going to pick whether it's
a square, rhombus, rectangle, parallelogram, trapezoid,
none of the above. And I'm assuming we're
going to pick the most specific one possible, because
obviously all squares are rhombuses, or rhombi,
I guess you'd say. Not all rhombi are squares. All squares are also rectangles. All squares, rhombi, and
rectangles are parallelograms. So we want to be as specific
as possible in picking this. So let's see, point
A is at 1 comma 6. I encourage you to
pause this video and actually try this on your
own before seeing how I do it, but I'll just proceed. So that's point A
right over there. Point B is at
negative 5 comma 2. That's point B. Point C is at-- just had
some carbonated water, so some air is coming up. Point C is at
negative 7 comma 8. So that is point C
right over there. And then finally, point
D is at 2 comma 11. And actually that kind
of goes off the screen. This is 10, 11 would
be right like this. So that would be 2 comma 11. If we were to extend
this, this is 10 and this is 11 right up here. 2 comma 11. So let's see what this
quadrilateral looks like. You have this line right
over here, this line right over there, that line
right over there, and then you have
this line like this, and then you have
this like this. So right off the bat, well it's
definitely a quadrilateral. I have four sides. But the key question, are
any of these sides parallel to any of the other sides? So just looking at it, side CB
is clearly not parallel to AD. You just can look at it. Now it also looks like
CD is not parallel to BA, but maybe I just drew it badly. Maybe they actually
are parallel. So let's see if we
can verify that. So the way to tell whether
two things are parallel is to actually figure
out their slopes. So let's first figure out
the slope of AB, or BA. So let's figure
out our slope here. Your slope is going
to be the change in y over your change in x. And in this case,
you could think of it as we're starting at the
point negative 5 comma 2, and we're ending at
the point 1 comma 6. So what's our change in y? Our change in y, we
go from 2-- we're going from 2 all the way to 6. Or you could say it's 6 minus
2, our change in y is 4. What's our change in x? Well we go from negative 5
to 1, so we increased by 6. Or another way of thinking
about it, 1 minus negative 5, well that's going
to be equal to 6. So our slope here is 2/3. It's 2/3. Every time we move 3
in the x direction, we go up 2 in the y direction. Move 3 in the x direction,
go up 2 in the y direction. Now let's think about
line CD up here. What is our slope? Our change in y over change
in x is going to be equal to, let's see. Our change in-- let's figure
out our change in x first. Our change in x, we're
going from negative 7 comma 8 all the
way to 2 comma 11. So our change in x, we're
going from negative 7 to 2. Or we could say 2
minus negative 7. So we are increasing by 9. That's our change in x. So that's going
to be equal to 9. And then our change in y, well
it looks like we've gone up. We've gone from 8 to
11, so we've gone up 3. Or we could say 11 minus 8. Notice, endpoint
minus start point. Endpoint minus start point. You have to do that on the
top and the bottom, otherwise you're not going to actually
be calculating your change in y over change in x. But you notice our change,
when our x increases by 9, our y increased by 3. So the slope here
is equal to 1/3. So these actually
have different slopes. So none of these lines are
parallel to each other. So this isn't even
a parallelogram. This isn't even a trapezoid. Parallelogram, you have to have
two pairs of parallel sides. Trapezoid, you have to have
one pair of parallel sides. This isn't the case for any of
these, or none of these sides are parallel. So we would go with
none of the above.