1 properties of lines and planes of solids chapter 4
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1
Properties of Lines and Planes of Solids
Chapter 4
2
Contents Perpendicular Line of a Plane Angle between a Line and a Plane Angles between Two Planes Making a Cuboid (For investigating
angles found in a cuboid)
3
Perpendicular Line of a Plane
4
Perpendicular Line of a Plane
Wooden Stick (Perpendicular Line)
Blue-Tack
5
Top View: The stick should coincide with the point O.
Stick
6
The stick is perpendicular to all 3 lines: OA, OB and OC.
Right Angle
7
From a different perspective
Right Angle
8
Again from another perspective
Right Angle
9
Top view
10
Angle between a Line and a Plane
Projection of OD on plane X(Line directly below stick)
D
Plane X
11
Top view – OD coincides with OA
D
12
Join AD – AD plane X
D
Plane X
13
DOA = Angle between Line OD and Plane X
D
Plane X
Angle between line OD and plane X
14
Another explanation
Light directly above stick
15
The light casts a shadow on the ground
D
Shadow of stick
Angle between stick and horizontal
plane
16
Top view
17
Angle between 2 planes
P
Q
18
Fold the black line to form 2 planes
wooden stick
P
Q
line of intersection of planes A and B
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Angle between Planes A and B
P
Q
Both PX and QX are line of intersection
PXQ = Angle between planes A and B
20
Another perspective
PXQ = Angle between planes A and B
21
Side view
PXQ = Angle between planes A and B
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Make a Cuboid - Your turn!
12 cm x 4
8 cm x 8
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Build the foundation
Paper
Blu-Tack
24
Build the foundation
Top view
25
Then build the first wall
26
Then the second wall
27
Finally complete the roof
28
From another perspective
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Top view
30
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Angle between red line and blue rectangle = ?
A
B
C
D
E
F
G
H
32A
B
C
D
E
FG
H
F
Angle between red line and blue rectangle = ?
33
Angle between BH and Plane ABCD =
A
B
C
D
E
F
G
H
Projection of BH on Plane ABCD = BC
HBC
HBC
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Angle between line AH and Plane ABCD
A B
C
D
E
F G
H
Projection of AH on Plane ABCD = ACHAC
35A B
CD
E
F G
H
Angle between line AH and Plane ABCD = HAC
36
Side View of HAC
A
C
H
37A B
CD
E
FG
H
Right Angles with G as Vertex (Type A)
FGH
FGBHGB
38A B
CD
E
FG
H
Right Angles with G as Vertex (Type B)(Involves a diagonal)
EGB
AGHFGC
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