Some technical terms to know about
A. Angle between two lines.
B. Angle between a line and a plane.
C. Intersection of two planes.
D. Angle between two planes.
E. A line of greatest slope.
A. Angle between two lines
Whenever
ambiguous,
always refer
to the acute
angle.

• A’ is the projection of the point A onto the
plane  if AA’ is perpendicular to 
A
A’

• Line segment A’B’is the projection of A on
the plane 
B

A
A’
B’
• If the line AB intersects the line at A, then
we say that B’ is the projection of B on 
and AB is the line of projection
B

A
B’
(a) If the line is parallel to the plane, we
cannot find the point of intersection
L

(b) A normal of a plane is a line perpendicular
to every line lying on the plane
L
L1
L2
L3
(c) If a line is not parallel to the plane, then
we can find the point of intersection.
L

B. Angle between a line and a plane
QN is a perpendicular to the plane ABCD.
PN is the projection of
Q
PQ on the plane ABCD
 is the angle between
A
the line PQ and the
D
plane ABCD.

N
P
B
C
Eg. Two walls which are
(a)Two parallel planes
1
2
opposite to each other
(b)
Line of intersection of the planes
1
2
E.g.
C. Angle between two planes
Find the line of
intersection.
Construct two lines
which lie on the planes
such that both of them
are perpendicular to the
line of intersection
Can you now define the angle
between two planes?
• If a horizontal plane which intersects an
inclined plane ( ) at AB and L is a line on
, L is the line of greatest slope on  if L is
perpendicular to AB.

L
A
B
• In the figure , XYAB and XYCD are two
intersecting planes which XYCD is inclined
and XYAB is horizontal , PQ is a line on
XYCD and perpendicular to XY。
• Notice that  > 
• The angle between the line of greatest slope
and the horizontal plane is also the angle
between the planes
Q
D
A
B
R

X
C

P
Y
O
Find the angle between OB
and ABCD.
What is the projection of
OB on the plane ABCD?
What is the
angle between
OB and ABCD?
C
D
N
A
B
O
Find the angle between ON and
plane OBC
What is the projection of
ON and plane OBC?
What is the
required angle?
C
D
N
A
M
B
O
Find the angle between planes
OBC and ABCD
What is the line of
intersection?
Draw a line on the plane
OBC and ⊥BC
Draw a line on the
plane ABCD and
⊥ BC.
D
C
N
What is the
required angle?
A
M
B
O
Find the angle between planes
ONB and ONM
What is the line of
intersection?
Draw a line on ONB
and ⊥ON
Draw a line on
ONM and ⊥ON
D
N
A
What is the
required angle?
C
M
B
Angle between planes OAB and OBC
O
What is the line of intersection?
Draw a line on OAB and⊥OB
Draw a line on OBC
and ⊥OB
C
D
What is the required
angle?
A
N
M
B
The End