The document describes activities to identify planes and angles between planes and lines using diagrams of cuboids. It includes examples of identifying: 1) Different planes of a cuboid labeled with points, such as the top plane EFGH and side plane ADHE. 2) The location of points relative to other points, such as point E being to the left of point F. 3) The angle between a line and plane using concepts like normal and orthogonal projections. 4) Calculating the measure of the angle between a line and plane using trigonometric functions. 5) Identifying the angle between two planes by selecting points that intersect both planes and constructing a triangle.

1. Prepared By Amobi Soft Copy
Pulishers 0706 851 439

2. A
B
C
D
E F
G
H
PLANE AT THE TOP : PLANE EFGH
ACTIVITY 1 : TO IDENTIFY THE PLANE
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

3. A
B
C
D
E F
G
H
PLANE ON THE LEFT : PLANE ADHE
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

4. A
B
C
D
E F
G
H
PLANE IN THE FRONT : PLANE ABFE
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

5. A
B
C
D
E F
G
H
PLANE AT THE BACK : PLANE DCGH
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

6. A
B
C
D
E F
G
H
PLANE AT THE BOTTOM: PLANE ABCD
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

7. A
B
C
D
E F
G
H
PLANE ON THE RIGHT : PLANE BCGF
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

8. ON TOP OF THE RED DOT
TO THE RIGHT OF
THE RED DOT
IN FRONT OF THE
RED DOT
AT THE BACK OF
THE RED DOT
THE LOCATION OF THE POINT
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

9. AT THE
BOTTOM OF ….
ON THE
TOP OF ….
AT THE
BACK OF ….
IN FRONT
OF ….
TO THE
LEFT OF ….
TO THE
RIGHT OF ….
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

10. ACTIVITY 2 : TO DETERMINE THE LOCATION OF A POINT
A B
C
D
E
F
G
H
POINT TO THE LEFT OF F : POINT E
POINT G
POINT AT THE BOTTOM OF F :
POINT AT THE BACK OF F :
POINT TO THE RIGHT OF D :
POINT ON TOP OF D :
POINT IN FRONT OF D :
POINT B
POINT C
POINT H
POINT A
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

11. ANGLE BETWEEN
A LINE AND A PLANE
A
B
C
LINE
PLANE
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

12. B
A
C
D
E F
Orthogonal
projection
Normal
H G
Activity 3 :To Identify The Angle Between Line And Plane
The line draw from
G and
perpendicular to
the plane ABCD is
call normal
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.
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.
 Prepared By Amobi Soft Copy
Pulishers 0706 851 439

13. B
A
C
D
E F
H G
ACTIVITY 3 : To Identify The Angle Between A Line And A Plane
A
G C

Angle between the line AG and the plane ABCD

At the bottom
Name the angle between the line
AG and the plane ABCD
Normal
Orthogonal
projection
Example 1a
= GAC. Prepared By Amobi Soft Copy
Pulishers 0706 851 439

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. Prepared By Amobi Soft Copy
Pulishers 0706 851 439

15. Diagram 2(a) shows a cuboid, ABCDEFG. Find the
angle between the line AH and the plane DCGH.
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
5cm
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

16. Draw the line AH and
shade the plan DCGH
in diagram 2a.
1.
Solutions
Steps
No
A
C
D
E
H G
F
5cm
4cm
12cm
B
Diagram 2a
Diagram 2a shows a cuboid, ABCDEFG. Find the angle between the line
AH and the plane DCGH.
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

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
H
A
back
D

5cm
B
A
C
D
E
H G
F
4cm
12cm
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

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
D
A


5cm
4cm
A H D

B
A
C
D
E
H G
F
12cm
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

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.
5cm
B
A
C
D
E
H G
F
4cm
12cm
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

20. No Steps Solutions
6 Mark,
- the opposite side, AD asT
- the adjacent side, HD as S
H
D
A
5 cm
4 cm
S
T
5cm
B
A
C
D
E
H G
F
4cm
12cm
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

21. No Steps Solutions
6 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
were known
Tan AHD =
AHD = tan -1
AHD = 38040’

– TOA
A
O
T
- SOH
H
O
S
– CAH
H
A
C

5
4


5
4
5cm
B
A
C
D
E
H G
F
4cm
12cm
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

22. example 2 (b)
Diagram 2b shows a cuboid,ABCDEFGH. Calculate
the angle between the line HB and the plane BCGF
A B
C
D
E F
G
H
4 cm
12 cm
3 cm
Diagram 2b
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

23. ANGLE BETWEEN TWO
PLANES
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

24. ACTIVITY 5 : To Identified The Angle Between Two
Planes
A
E
B
C
D
H G
F
Diagram 3a
Diagram 3a shows a cuboid,
ABCDEFGH. Name the angle between
the plane AGH and the plane ABCD
1.DRAW 3 LINES
EXAMPLE 3(a)
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

25. B
A
C
D
E
H G
F
Diagram 3a
Bottom
2.Mark the location
(direction) of the
plane ABCD at the
bottom of the first
line to the left.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid,
ABCDEFGH. Name the angle
between the plane, AGH and the
plane, ABCD
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

26. B
A
C
D
E
H G
F
Diagram 3a
A
Bottom
3.Refer to the plane,
AGH, identify the
points which
touch the plane,
ABCD and write it
at the middle line.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid,
ABCDEFGH. Name the angle
between the plane, AGH and the
plane, ABCD
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

27. B
A
C
D
E
H G
F
Diagram 3a
A
H / G
Bottom
3.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.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid,
ABCDEFGH. Name the angle
between the plane, AGH and the
plane, ABCD
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

28. B
A
C
D
E
H G
F
Diagram 3a
A
H/G
Bottom
5.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.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid,
ABCDEFGH. Name the angle
between the plane, AGH and the
plane, ABCD
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

29. B
A
C
D
E
H G
F
Diagram 3a
A
H
Ke Bawah
5.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.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid,
ABCDEFGH. Name the angle
between the plane, AGH and the
plane, ABCD
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

30. B
A
C
D
E
H G
F
Diagram 3a
A
H
Bottom
D

6. Identify the point
which is located at
the bottom of the
point H ( )and
write it on the first
line to the right.
Diagram 3a shows a cuboid,
ABCDEFGH. Name the angle
between the plane, AGH and the
plane, ABCD
ACTIVITY 5 : To Identified The Angle Between Two Planes
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

31. B
A
C
D
E
H
G
F
Diagram 3a
Bottom
A
H D


7.In the diagram 3a,
complete the ∆ HAD
and mark the HAD
Angle between the plane, AGH and the plane, ABCD
= HAD


ACTIVITY 5 : To Identified The Angle Between Two Planes
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

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
Prepared By Amobi Soft Copy
Pulishers 0706 851 439

33. THANK YOU
Prepared By Amobi Soft Copy
Pulishers 0706 851 439