Geometry
Notes 11-1
Points, Lines, Planes,
Perpendicular Lines and Planes,
Parallel Lines and Planes.
Parallel Lines in Space: are lines in the same plane that have no points in common.
Theorem 11.2: If two lines intersect, then there is exactly one plane containing them.
Skew Lines: are lines in space that are neither parallel nor intersecting.
Postulate 11.3: If two planes intersect, then they intersect in exactly one line.
Theorem 11.4: 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 these lines.
Dihedral Angle: is the union of two half planes with a common edge.
Measure of a Dihedral angle:is the measure of the plane angle formed by two rays each
in different half planes of the angle and each perpendicular to the common edge at the
same point of the edge.
1
Perpendicular planes: are two planes that intersect to form a right
dihedral angle.
A line is perpendicular to a plane if and only if it is perpendicular to each
line in the plane through the intersection of the line and the plane.
A plane is perpendicular to a line if the line is perpendicular to the plane.
Theorem 11.7 - Through a given point on a line, there can be only
one plane perpendicular to the given line.
2
Ex. 1 Show that the following statement is false:
Two planes perpendicular to the same plane have no points in common.
Pull
Ex. 2 Planes p and q intersect in line AB. In p,
if
, is
?
and in q,
D
q
p
A
B
C
Parallel Planes: are planes that have no points in common
Theorem 11.12: Two planes are perpendicular to the same line if and only if
the planes are parallel.
Distance between two planes: the length of the line segment perpendicular to
both planes with an endpoint on each plane.
Ex. 3 Line m is perpendicular to plane p and line m is not perpendicular to
plane q. Is p parallel to q?
p
q
m
3