Points Lines & Planes
Section 1.4
Point: a location in space
Represented
by a capital letter
Symbol: .
Example: . D
The
name of this example is point D or just D
Line: a set of points that extends infinitely in two
directions
Represented
by drawing a straight line and naming any two points on the line
Symbol:
Example:
To name
a line you must name any two points on the line and include the symbol above
the two points OR you can name a line by using a single lower case
letter.
The name of this example line is l
The name
of this example line is AB or AC
or AD or
BC or BD
or CD
or . . .
You
must have at least two points in order to have a line!
For
any two points, there is exactly one line through these points.
Points
that are all on the same line are collinear.
You
can draw one straight line through all collinear points.
Plane: A flat surface that extends infinitely in all
directions
Represented by drawing a square or rectangle and
naming any
three non-collinear
points on the plane
Non-collinear points:
points that are not in the
same line, you
can not
draw one
straight line through all non-collinear points.
Example:
To name
a plane you must name any three non-collinear points
on the plane
or by naming the plane using a capital letter.
The
name of this example plan is
S or
The
name of this example is plane GHI or plane IHJ or plane GJH or . . .
You
must have at least three non-collinear points on have a Plane!
Points
and other figures that lie in the same plane are coplanar
If
two different figures share at least one point, then they intersect.
The
point or points two figures share are called the intersection.
Two
lines intersect at only one point
A
line and a plane intersect at only one point
Two
planes intersect at only one line
If
two lines in the same plane do not interest, then they are parallel.
The
symbol for parallel lines
·
Red Arrows show that lines are parallel in a
sketch
·
| |
two straight line show that lines are parallel when written
between the names of
those line. Example m | | l or
BE | | FG
If
two lines do not interest and are not parallel then they are skew.
Skew lines: Two lines that
do not lie in the same plane (therefore, they cannot be parallel or intersect).
The picture of skewed lines
is from http://www.intermath-uga.gatech.edu/dictnary/descript.asp?termID=424