properties of lines and planes of solids
DESCRIPTION
Properties of Lines and Planes of Solids. Chapter 4. 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). Perpendicular Line of a Plane. Perpendicular Line of a Plane. Wooden Stick - PowerPoint PPT PresentationTRANSCRIPT
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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
19
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
22
Make a Cuboid - Your turn!
12 cm x 4
8 cm x 8
23
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
29
Top view
30
31
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
34
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