1. LINES AND PLANES IN
THREE DIMENSIONS

2. ACTIVITY 1 : TO IDENTIFY THE PLANEG E F D C A B
PLANE AT THE TOP :
PLANE EFGH

3. H G E F D C A B
PLANE ON THE LEFT :
PLANE ADHE

4. H G E F D C A B
PLANE IN THE FRONT :
PLANE ABFE

5. H G E F D C A B
PLANE AT THE BACK :
PLANE DCGH

6. H G E F D C A B
PLANE AT THE BOTTOM:
PLANE ABCD

7. H G E F D C A B
PLANE ON THE RIGHT :
PLANE BCGF

8. THE LOCATION OF THE POINT
ON TOP OF THE RED DOT
TO THE RIGHT OF THE RED DOT
AT THE BACK OF THE RED DOT
IN FRONT OF THE RED DOT

9. ON THE TOP OF ….
AT THE BACK OF ….
TO THE LEFT OF ….
TO THE RIGHT OF ….
IN FRONT OF ….
AT THE BOTTOM OF ….

10. ACTIVITY 2 : TO DETERMINE THE LOCATION OF A POINTB C D E F G H
POINT TO THE LEFT OF F :
POINT E
POINT AT THE BOTTOM OF F :
POINT B
POINT AT THE BACK OF F :
POINT G
POINT TO THE RIGHT OF D :
POINT C
POINT ON TOP OF D :
POINT H
POINT IN FRONT OF D :
POINT A

11. ANGLE BETWEEN A LINE AND A PLANEC

12. Orthogonal projection
Activity 3 :To Identify The Angle Between Line And Plane H G
The line draw from G and perpendicular to the plane ABCD is call normal
Normal E F D C
The line lies on the plane ABCD which joint the point A to the line GC is known as the orthogonal projection of line AG on the plane ABCD.
Orthogonal projection A B
The angle between the line AG and the orthogonal projection, AC is the angle between the line AG and the plane ABCD that is
GAC.

13. Angle between the line AG and the plane ABCD
ACTIVITY 3 : To Identify The Angle Between A Line And A Plane
Example 1a H G G A C
Normal E F D C
At the bottom
Name the angle between the line AG and the plane ABCD A B
Orthogonal projection
Angle between the line AG and the plane ABCD
= GAC.

14. EXAMPLE 1(b) B A C D E H G F
Diagram 1(b)
Diagram 1b shows a cuboid ABCDEFGH. Name the angle between the line HB and the plane ABCD.

15. To find the angle between a line and a plane
ACTIVITY 4 :
To find the angle between a line and a plane
Example 2(a)
5cm B A C D E H G F
4cm
12cm
Diagram 2a
Diagram 2(a) shows a cuboid, ABCDEFG. Find the angle between the line AH and the plane DCGH.

16. No
Steps
Solutions 1.
Draw the line AH and shade the plan DCGH in diagram 2a.
12cm H G
5cm E F D C
4cm A B
Diagram 2a
Diagram 2a shows a cuboid, ABCDEFG. Find the angle between the line AH and the plane DCGH.

17. No
Steeps
Solutions 2
Use the method you have learned in activity 3, identify the angle between the line AH and the plane DCGH A H D
back
5cm B A C D E H G F
4cm
12cm

18. No
Steps
Solutions 3
Refer to the points you have obtained in steep 2 (point A, H, D), complete the ∆ AHD. Mark
AHD. Mark the right angle,
HDA. Transfer out the
∆ AHD. H A D H
12cm G A H D
5cm E F D C
4cm A B

19. No
Steps
Solutions 4
With the information given in the question, label the length of the sides of ∆ AHD. At least the length for 2 sides must be known. Use Pythegoras Theorem if necessary. H
5 cm A D
4 cm H
12cm G
5cm E F D C
4cm A B

20. No Steps Solutions 6 H Mark, - the opposite side, AD asT
- the adjacent side, HD as S
5 cm S A D
4 cm T
5cm B A C D E H G F
4cm
12cm

21. 6 No Steps Solutions Use the tangent formula to calculate AHD.
Remember, use
The sine formula, if O and H were
known
- The cosine formula, if A and H
were known
The tangent formula, if O and A
Tan AHD =
AHD = tan -1
AHD = ’
- SOH
– CAH
5cm B A C D E H G F
4cm
12cm
– TOA

22. example 2 (b)
12 cm H G E F
4 cm D C
3 cm A B
Diagram 2b
Diagram 2b shows a cuboid,ABCDEFGH. Calculate the angle between the line HB and the plane BCGF

23. ANGLE BETWEEN TWO PLANES

24. DRAW 3 LINES ACTIVITY 5 : To Identified The Angle Between Two Planes
EXAMPLE 3(a) G H E F D C
DRAW 3 LINES A B
Diagram 3a
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane AGH and the plane ABCD

25. ACTIVITY 5 : To Identified The Angle Between Two Planes
Bottom A B
Mark the location (direction) of the plane ABCD at the bottom of the first line to the left.
Diagram 3a
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

26. ACTIVITY 5 : To Identified The Angle Between Two Planes
Bottom A
Refer to the plane, AGH, identify the points which touch the plane, ABCD and write it at the middle line. B
Diagram 3a
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

27. ACTIVITY 5 : To Identified The Angle Between Two Planes
H / G A E F D C
Bottom
Refer to the plane, AGH, identify the point which does not touch the plane, ABCD and write it at the first line to the left. A B
Diagram 3a
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

28. ACTIVITY 5 : To Identified The Angle Between Two Planes
H/G A
Bottom E F D C
Between the point H and G, point which is nearer to point A or located on the same plane as point A will be choosen. Point which is not choosen will be earased. A B
Diagram 3a
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

29. ACTIVITY 5 : To Identified The Angle Between Two Planes
Ke Bawah E F D C
Between the point H and G, point which is nearer to point A or located on the same plane as point A will be choosen. Point which is not choosen will be earased. A B
Diagram 3a
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

30. ACTIVITY 5 : To Identified The Angle Between Two Planes
Bottom E F D C
Identify the point which is located at the bottom of the point H ( )and write it on the first line to the right. A B
Diagram 3a
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD

31. ACTIVITY 5 : To Identified The Angle Between Two Planes
Bottom
In the diagram 3a, complete the ∆ HAD and mark the HAD A B
Diagram 3a
Angle between the plane, AGH and the plane, ABCD
= HAD

32. EXAMPLE 3(b)
Diagram 3b E
5cm B A C D H G F
4cm
12cm
Diagram 3b shows a cuboid with horizontal rectangle base ABCD. Name the angle between the plane ACH and the plane CDHG

33. THANK YOU