properties of lines and planes of solids

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1 Properties of Lines and Planes of Solids Chapter 4

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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 Presentation

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Page 1: Properties of Lines and Planes of Solids

1

Properties of Lines and Planes of Solids

Chapter 4

Page 2: Properties of Lines and Planes of Solids

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)

Page 3: Properties of Lines and Planes of Solids

3

Perpendicular Line of a Plane

Page 4: Properties of Lines and Planes of Solids

4

Perpendicular Line of a Plane

Wooden Stick (Perpendicular Line)

Blue-Tack

Page 5: Properties of Lines and Planes of Solids

5

Top View: The stick should coincide with the point O.

Stick

Page 6: Properties of Lines and Planes of Solids

6

The stick is perpendicular to all 3 lines: OA, OB and OC.

Right Angle

Page 7: Properties of Lines and Planes of Solids

7

From a different perspective

Right Angle

Page 8: Properties of Lines and Planes of Solids

8

Again from another perspective

Right Angle

Page 9: Properties of Lines and Planes of Solids

9

Top view

Page 10: Properties of Lines and Planes of Solids

10

Angle between a Line and a Plane

Projection of OD on plane X(Line directly below stick)

D

Plane X

Page 11: Properties of Lines and Planes of Solids

11

Top view – OD coincides with OA

D

Page 12: Properties of Lines and Planes of Solids

12

Join AD – AD plane X

D

Plane X

Page 13: Properties of Lines and Planes of Solids

13

DOA = Angle between Line OD and Plane X

D

Plane X

Angle between line OD and plane X

Page 14: Properties of Lines and Planes of Solids

14

Another explanation

Light directly above stick

Page 15: Properties of Lines and Planes of Solids

15

The light casts a shadow on the ground

D

Shadow of stick

Angle between stick and horizontal

plane

Page 16: Properties of Lines and Planes of Solids

16

Top view

Page 17: Properties of Lines and Planes of Solids

17

Angle between 2 planes

P

Q

Page 18: Properties of Lines and Planes of Solids

18

Fold the black line to form 2 planes

wooden stick

P

Q

line of intersection of planes A and B

Page 19: Properties of Lines and Planes of Solids

19

Angle between Planes A and B

P

Q

Both PX and QX are line of intersection

PXQ = Angle between planes A and B

Page 20: Properties of Lines and Planes of Solids

20

Another perspective

PXQ = Angle between planes A and B

Page 21: Properties of Lines and Planes of Solids

21

Side view

PXQ = Angle between planes A and B

Page 22: Properties of Lines and Planes of Solids

22

Make a Cuboid - Your turn!

12 cm x 4

8 cm x 8

Page 23: Properties of Lines and Planes of Solids

23

Build the foundation

Paper

Blu-Tack

Page 24: Properties of Lines and Planes of Solids

24

Build the foundation

Top view

Page 25: Properties of Lines and Planes of Solids

25

Then build the first wall

Page 26: Properties of Lines and Planes of Solids

26

Then the second wall

Page 27: Properties of Lines and Planes of Solids

27

Finally complete the roof

Page 28: Properties of Lines and Planes of Solids

28

From another perspective

Page 29: Properties of Lines and Planes of Solids

29

Top view

Page 30: Properties of Lines and Planes of Solids

30

Page 31: Properties of Lines and Planes of Solids

31

Angle between red line and blue rectangle = ?

A

B

C

D

E

F

G

H

Page 32: Properties of Lines and Planes of Solids

32A

B

C

D

E

FG

H

F

Angle between red line and blue rectangle = ?

Page 33: Properties of Lines and Planes of Solids

33

Angle between BH and Plane ABCD =

A

B

C

D

E

F

G

H

Projection of BH on Plane ABCD = BC

HBC

HBC

Page 34: Properties of Lines and Planes of Solids

34

Angle between line AH and Plane ABCD

A B

C

D

E

F G

H

Projection of AH on Plane ABCD = ACHAC

Page 35: Properties of Lines and Planes of Solids

35A B

CD

E

F G

H

Angle between line AH and Plane ABCD = HAC

Page 36: Properties of Lines and Planes of Solids

36

Side View of HAC

A

C

H

Page 37: Properties of Lines and Planes of Solids

37A B

CD

E

FG

H

Right Angles with G as Vertex (Type A)

FGH

FGBHGB

Page 38: Properties of Lines and Planes of Solids

38A B

CD

E

FG

H

Right Angles with G as Vertex (Type B)(Involves a diagonal)

EGB

AGHFGC