Transcript Lines: What are they good for anyway?

Points, Lines, and Planes
The Three Undefined Terms of
Geometry
A point is an exact location in space.
You are here.
A true point has no length, no width,
and no height.
In fact, you cannot see a true point.
A point is named by a letter.
Point P
P
Lines are 1-dimensional objects
that have only length. Lines
continue forever in both
directions.
Because a line has no width or
height, you cannot see a true line.
A line is defined by 2 points.
A
B
Line AB
A ray has a starting point but no
ending point.
A ray of light has a starting point
(like the sun) and continues
forever in the same direction.
Of course, if the ray hits an
object, the light could be
absorbed or reflected.
MIRROR
A ray is also defined by 2 points.
C
D
Ray CD
A line segment has a starting
point and an ending point. Line
segments can be measured.
A line segment also defined by 2
points.
E
F
Line Segment EF
Lines can do various things.
Lines can intersect at a point to
form angles.
X
Y
Z
Angles are defined by 3 points.
X
Y
Z

XYZ
These angles can be right angles.
90 
These angles can be right angles.
R
m USR = 90⁰
m RST = 90⁰
c
U
S
m USV = 90⁰
T
m TSV = 90⁰
V
When lines intersect to form right angles, they
are said to be perpendicular.
UT

RV
R
c
U
S
V
T
Lines can intersect to form acute
and obtuse angles.
45 acute
135
obtuse
Lines can also run into each other
to form straight angles.
180  is a straight angle
Lines do not always intersect.
Lines can be parallel.
Parallel lines have the same slope
or steepness.
Is it possible for lines not to
intersect and not be parallel
either?
Believe it or not, this is possible.
Let’s consider a 3-dimensional
rectangular prism.
These 2 lines are not parallel, but
they are not intersecting either.
These lines are called skew lines.
You might have heard the word
“skewer” the last time you had a
barbecue.
S
K
E
W
E
R
A skewer raises your “dinner” off
the surface of the grill. The
skewer does not intersect the
grill, and the skewer is not
parallel to the grill.
Lines can be…
intersecting
parallel
perpendicular
90º
skew
A plane
is a flat
surface that has
length & width
but no height.
You can see a plane only if you view
it at a certain angle.
A true plane goes on forever in all
directions.
A true plane goes on forever in all
directions.
A true plane goes on forever in all
directions.
A true plane goes on forever in all
directions.
A true plane goes on forever in all
directions.
Planes can…
Planes can
intersect.
An X-Wing fighter from Star Wars
has wings that intersect.
Planes can
be perpendicular.
Planes can
be parallel.
A Tie Fighter from Star Wars has
wings that are parallel.
Planes can be…
intersecting
parallel
perpendicular
The end.