all right hello everybody
my name is ms. Suchy and i'm going to be
going through the geometry lesson 1.1
notes today.
at the top of each of your notes pages
you will see that we have
our objectives listed and those are
always telling us what
the goals are of this lesson. so for this
lesson
we're looking at the terminology,
which is the vocabulary, and then the
symbols used in that vocabulary
for geometry. we're also looking at
figures
being able to identify and label the
figures
and then also being able to define those
figures and sketch them.
so first task for you is to
describe what geometry means in your own
words.
all right now if we were to break down
the word we have the word
geo which means earth
and metres means measure
and when we put geometry together
it means the study of earth's measure.
all right now geometry is used in a
lot of things
you might see some people working
on the road
with those little tripods and they're
looking through like a little camera
what they're doing is looking for
boundary lines
and landmarks and things so that they
can make sure
that all of their structures and roads
and things are correct.
the egyptians also did this and they did
it when the nile river would
flood. so it would change the landscape a
little bit
but they would use geometry to figure
out, oh yeah this was my yard and this
was your yard.
so the Egyptians were using this way
earlier.
i can never spell Egyptians.
there we go. okay now if we were to look
in webster,
webster has an official definition. it
says that math
is a, i'm sorry, geometry is a branch
of
math
and it looks at a lot of things. so it
looks at
measurements,
points, lines,
angles,
solids, surfaces.
let me see if i'm missing anything...
and the relationships and properties of
those.
all right, so now that we've covered what
geometry means we're actually going to
dive into it and study
those things those points lines angles
solid surfaces measurements and
all different things that are related to
geometry.
so on the right here begins our
vocabulary, or our terminology.
so each of these words is going to have
some sort of visual that goes with it,
it's going to have some sort of
annotation with it, so
markings and certain ways of writing
things, and then we'll have some sort of
definition or properties that go with it.
so to be a point you've seen points in
algebra a lot.
points are like coordinate points where
you have a dot
and when you have a coordinate point or
a point
you're always naming it with a capital
letter. so maybe i'll put
letter p for point so they're named with
capital letters.
all right now the definition of a point
is a location
that has no specific size
and again it's represented by that dot
and a capital letter.
the point is one of the main building
blocks of geometry because everything is
made up of points.
all right the next word, line.
so line seems like a simple geometry
word
but it has a very specific definition in
geometry itself.
so to be a line you have to be straight,
you have to be continuous, which means
there can't be any breaks in it,
and you go on infinitely forever
in two directions. so it is a
straight
and continuous
arrangement of infinitely many points.
so it's actually if you were to zoom in
really close
on that line you would see point point
point point point
all smashed together. so they're
all going together in that same
direction both to the right
and to the left. in this case so the
properties of it
are that they are infinite
and they go in two directions.
okay now when we name a line we're
actually naming
some of the points on the line. so even
though there's infinite number of points
on here i'm going to emphasize
just two of them and it can be anywhere
on the line.
whenever i have a point i have to
name it with a capital letter
so i'll just do a and b. then for our
line
we're naming it with two capital letters.
which are our points and we kind of just
smash those two letters together. so
a and b (i could reverse them if i wanted
to ba).
that would work too. and then above
that to represent the line itself and
not just two separate points we actually
make a little mini picture of a line.
that's it. all right the next one
a plane. now a plane
is actually kind of like a piece of
paper
where it's a flat surface and it's where
we can put all of our lines and points
on. but if you're thinking
three-dimensionally in our world here,
we have planes everywhere, we just don't
have specific walls
showing those planes. but you can think
of
there's a layer in all of this space
around us
and each layer might have different
points on it depending what's in that
layer.
so what we're going to represent a plane
with is
like a sheet of paper.
so an example of a plane is paper
and this gives us a space a flat
surface um that has a width and a
length but it's not a specific thickness and it allows us to draw on
all of our geometry things in a plane. so
plane has a
width and length
but no thickness it's a flat
surface that extends infinitely in both
directions.
when we name a plane, because it has so
many points on it,
we do name it with a capital letter but
we're not emphasizing
one specific point so that capital
letter has to be cursive.
i stink at cursive letters, so
i just do a capital letter and then i
make it look fancy
to make it look cursive. so it's named
with a
capital
cursive
letter.
all right our next term is the term
definition, which is kind of weird
because we are
making definitions for all of these
terms.
so a definition means an official
statement
that clarifies or explains the meaning
of a word
without using that word. so i wouldn't
want to say
a plane is a plane that's flat
because that would be using the word in
the definition. now i don't have a
picture here but if you want to draw a
dictionary
feel free.
all right our next set of words is on
the next page you have to flip that over
if you're following along.
the next two words collinear and
coplanar
are very similar they both start with
this co,
and if you think of couples, a couple of
people,
they are together. so co
is kind of like they're together and
then we have the
ending of the words, linear means line,
planar means plane, so collinear means
points on the same
line whereas coplanar means
points on the same
plane. so what i'm going to do is i'm
going to draw a line and a plane
and then i'm going to put some points on
there.
so these points here on the line are all
collinear a, b, and c.
and these points on the plane here are
all coplanar.
i'll call those a, b, and c,
but then i'm going to give you an
example of one that's not
on the plane or not on the line. so over
here
we got point d he is not on the same
line so he is
not collinear and
over here we've got point d on a
different
plane again not coplanar with points a b
and c.
so on this one, points a b and c are the
ones that are coplanar
d is not coplanar with them.
all right we've already talked about
lines but now when we have a line
segment. a segment is a portion of
something.
so we're going to take that line and
we're going to chop out a portion
and when you chop out a portion you get
a start and a stop
and those are called our end points. so
here would be an example
of a line segment and i don't ever
really use "line segment" as the full word
i just usually
say "segment." but a line segment consists
of
two points
called endpoints
and even though those are the two
emphasized points remember
all of this portion of that original
line is just point after point after
point.
and so it's all of those collinear
points
between them.
so those points in between the two
endpoints are on that same straight
portion
they are collinear with the end points.
all right so now i'm going to name this
like a line so i'm going to give those
points capital letters.
now for a segment we want to name the
two
end points so that we know exactly where
it starts and stops.
but we're going to name it kind of the
same as a line you just smash those two
letters together.
and this time our symbol [picture] doesn't have
any arrows so i make that same
symbol above the two points.
all right our next term is congruent
line segments
and that means obviously more than one
segment.
so i'm going to make two and the word
congruent means that they are the exact
same size and shape.
so segments have a clear definition of
what they are so we just need the
two segments that are the exact same
size. now i didn't measure this i'm kind
of eyeballing it,
but i purposely drew them going in
different directions because
where they're placed it does not matter.
they just have to have the same
measurement or the same length. so line
segments are congruent if and only if
they have
the same
length or measurement.
all right now i could take a ruler and
measure and say oh that's five
centimeters and this one's five
centimeters.
but in math we have a lot of notation
that you can also use.
so maybe i don't have a ruler handy but
i do know that they're the same length.
so by putting in hash marks that are
identical
on both figures it is referencing that
they are the same length.
so identical hash marks represent congruent segments.
now i can also write this as a math
statement, so let's call this one
segment ab and this one segment cd.
i can write that segment ab
is the same length as segment cd.
or they are congruent, and the symbol for
congruent
is an equal sign with a squiggly above
it.
so this right here is the symbol for the
word
congruent. so this is called a math
sentence.
all right over on the top right we're
going to start with the word midpoint.
and again has the word "point" in there so
obviously we're dealing with a point.
and if i think of the part "mid" i'm
thinking of middle.
so to be in the middle of something you
have to have something that is
a segment, of something a start and a
stop.
so i'm going to draw a segment
and to be the mid point it would have to
be in
the middle. now if it is in the middle
that would mean that it is the same
distance
from both points, where it is equidistant
from both end points. now i can again
take a ruler and measure
or i could just use some markings. so by
having the same two congruent set of
markings here
i'm saying that these two parts are in
fact equal.
so the midpoint of a segment
is the point on the segment that is the
same
distance from both
end points.
okay now again if i needed to reference
lengths here i could
label these points and i could say that
segment ab is congruent to
segment bc because they are the same
length.
all right now the next word bisect.
the prefix "bi" means
two, and then if you think of science
where you're dissecting something you're
kind of cutting it
open and inspecting it. bisect's kind
of the same way.
so we're cutting it into two equal parts
which is exactly what we did up here for
midpoint.
so you could copy the exact same picture
because a midpoint
bisects a segment, but it doesn't have to
be a
midpoint that does it. it could be
a line that's slicing through the
segment
at the midpoint. so i'm going to draw a
different example just so you have some
variety here.
so here we'll do ac again
we're still going to slice through the
middle of this so i can still call this
b, but maybe this time i'm going to slice
it
with a line instead of just the point
itself.
now because this is getting bisected it
does mean
that those two halves are the same. so
bisected means
to cut in half
or you could say into two
congruent parts.
all right moving on to the next word, ray.
a ray is another portion of a line,
however it is not a segment. it's kind of
like a
ray of sunshine. so if i think of a sun,
these rays start at the sun and come out,
and so i'm starting at a location and
then i'm going in a
certain direction. so this is called a
ray.
where it contains an endpoint
and then all of these points that are
going in that same direction
one side of the endpoint.
so they're all collinear.
ah i'm having troubles.
all right now when we name a ray we have
one point already emphasized so maybe
i'll call that
A and then we have to emphasize
one more point on that ray so that we
have
evidence that it's not just a point
we're talking about.
so i'm going to call this one b.
okay now the only tricky part with a ray
is that
you have to name it starting with the
endpoint letter.
so this is the important letter that has
to come first.
so i'm going to start with the letter A
and then i would put the next
letter that i chose or the next point.
sometimes they have multiple points [emphasized]
here, you only need two.
and then i would use that ray symbol
right above it.
so it's named with two capitals again
and again a ray is a portion of a line.
all right on the next page you can see
that we have a summary.
so this summary is going to be used the
following day to
recap our learning and to get our brains
thinking about that material again.
so we're going to save this summary for
tomorrow
and then when you fill it out tomorrow
it'll be a good
judge of: if you've remembered things, if
you need to review things,
if you didn't understand something and
you need to take some more notes.
it'll also give us some chances to do
some practice problems. so we will review
this the next day
and that's it for lesson 1.1.
 
