Name: ______________________________
Integrated Geometry – H
Date: ___________________
Planes
PLANE (an undefined term)
In geometry, a plane has no thickness
but extends indefinitely in all
directions. Planes are usually
represented by a shape that looks like a
tabletop or a parallelogram. Even
though the diagram of a plane has
edges, you must remember that the
plane has no boundaries. A plane is
named by a single letter (plane m) or
by three non-collinear points (plane
ABC).
Collinear Points
points that lie on the same line.
Coplanar points
points that lie in the same plane.
Opposite rays
2 rays that lie on the same line, with a common
endpoint and no other points in common. Opposite
rays form a straight line and/or a straight angle
(180°:).
Parallel lines
two coplanar lines that do not intersect
Skew lines
two non-coplanar lines that do not intersect.
Consider the following theorems relating lines and planes. A
diagram is supplied for each theorem that represents one
possible depiction of the situation.
If a line is perpendicular to each of two
intersecting lines at their point of
intersection, then the line is perpendicular
to the plane determined by them.
Through a given point there passes one
and only one plane perpendicular to a
given line.
Through a given point there passes one Two lines perpendicular to the same plane
and only one line perpendicular to a given
are coplanar.
plane.
Two planes are perpendicular to each
other if and only if one plane contains a
line perpendicular to the second plane.
If a line is perpendicular to a plane, then
any line perpendicular to the given line at
its point of intersection with the given
plane is in the given plane.
If a line is perpendicular to a plane, then
every plane containing the line is
perpendicular to the given plane.
If a plane intersects two parallel planes,
then the intersection is two parallel lines.
If two planes are perpendicular to the
same line, they are parallel.
The angle where two planes meet is called a dihedral angle.
PRACTICE PROBLEMS
1.) Which of the following are skew lines?
Choices:
A.
and
B.
and
C.
and
D.
and
2.) Name a plane that is parallel to Plane ABCD.
3.) Now try answering these questions on your own, using the diagram.
1. Are AD and FG in the same plane?
2. Name all the segments parallel to HG .
3. Name all segments skew to AD .
4.)
5.)
6.)
7.)
8.)
9.)
10.)
11.)
12.)
13.)
14.)
15.)