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

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