ACTIVITY SHEET Pupil’s Copy
Lesson 104: Horizontal Planes, Vertical Planes and Inclined Planes.
Plane Type of planes
EDIJ
ABGF
BGHC
ABCDE
CHID
Plane Type of planes
ABCD
AEB
BCFE
B
G H I
J
E
A D
F
C
Based on the figure given above, identify the type of planes for: Question 1
A
B E F
C D
Question 2
2
Plane Type of planes
AFB
CFD
ABCD
Plane Type of planes
ABFE
EFGH
ABCD Question 3
A B
C D
F
E
Question 4
A B
F E
C G H
D
Based on the figure given above, identify the type of planes for:
ACTIVITY SHEET Teacher’s Copy
Lesson 104: Horizontal Planes, Vertical Planes and Inclined Planes.
Plane Type of planes
EDIJ Inclined plane
ABGF Horizontal plane
BGHC Vertical plane
ABCDE Vertical plane
CHID Horizontal plane
Plane Type of planes
ABCD Vertical plane
B
G H I
J
E
A D
F
C
Based on the figure given above, identify the type of planes for: Question 1
A
B E F
C D
Question 2
4
BCFE Vertical plane
Plane Type of planes
AFB Inclined plane
CFD Inclined plane
ABCD Horizontal plane
Plane Type of planes
ABFE Vertical plane
EFGH Horizontal plane
ABCD Horizontal plane Question 3
A B
C D
F
E
Question 4
A B
F E
C G H
D
Based on the figure given above, identify the type of planes for:
ACTIVITY SHEET Pupils’ Copy
Lesson 105: Lines on a Plane, Lines Intersect with a Plane and Normals.
A D
C B
F G
H E
1. Name all the lines that lie on the plane CDHG.
Answer:
2. Name all the lines that intersect with the plane BCGF.
Answer :
3. Name all the normals to the plane ABFE
Answer : Question 1
Q R P
S U
T V
W
1. Name all the lines that lie on the plane RQTU.
Answer:
2. Name all the lines that intersect with the plane PQTS.
Answer :
3. Name all the normals to the plane STU
Answer : Question 2
1. Name all the lines that lie on the plane ABHG.
Answer:
2. Name all the lines that intersect with the plane FAGL.
Answer :
3. Name all the normals to the plane ABCDEF
Answer : Question 3
1. Name all the lines that lie on the plane ABCD.
Answer:
2. Name all the lines that intersect with the plane LKOP.
Answer :
3. Name all the normals to the plane EFGH Question 4
A B
C D E
F G
2 ACTIVITY SHEET
Teacher’s Copy
Lesson 105: Lines on a Plane, Lines Intersect with a Plane and Normals.
A D
C B
F G
H E
1. Name all the lines that lie on the plane CDHG.
Answer:
2. Name all the lines that intersect with the plane BCGF.
Answer :
3. Name all the normals to the plane ABFE
Answer :
Line: CD, DH, HG, GC, DG
Line: BA, CD, GH, FE, GD
Line: AD, BC, FG, EH Question 1
Q R P
S U
T V
W
1. Name all the lines that lie on the plane RQTU.
Answer:
2. Name all the lines that intersect with the plane PQTS.
Answer :
3. Name all the normals to the plane STU
Answer :
Line: RQ, QT, TU, UR, WV
Line: QR, VW, TU, PR, SU
Line: SP, UR, TQ Question 2
1. Name all the lines that lie on the plane ABHG.
Answer:
2. Name all the lines that intersect with the plane FAGL.
Answer :
3. Name all the normals to the plane ABCDEF
Answer :
Line: AB, BH, HG, GA
Line: AB, GH, LK, FE
Line: AG, BH, CI, DJ, EK, FL Question 3
1. Name all the lines that lie on the plane ABCD.
Answer:
2. Name all the lines that intersect with the plane LKOP.
Answer :
3. Name all the normals to the plane EFGH
Answer :
Line: AB, BC, CD, DA, IJ, JK, KL, LI
Line: LI, KJ, PM, ON
Line: EA, FB, GC, HD Question 4
A B
C D E
F G
ACTIVITY SHEET Pupil’s Copy
LESSON 106: Orthogonal projection of a line on a plane.
1. The figure shows a triangular prism PQRSTU. Draw and name the orthogonal projection of each of the following lines on the plane PQRS.
T
P
Q
R
S
U
M
N
a)
TQ
2
2. The figure shows a cube ABCDEFGH. Based on the diagram given, complete the table below.
Line Plane Orthogonal
Projection
Angle between line and plane
1 AG ABCD
2 HB ABEF
3 CH EFGH
4 EG DCHG
5 HB BCFG
A
B
C
D
E
F
3. The figure shows a pyramid ABCDEFG. Based from diagram given, complete the table below.
No Line Plane Angle between line and plane
1 ABCD EFG or GFE
2 ABCD EAC or CAE
3 ABCD EBD or DBE
4 ABCD EGF or FGE
5 ABCD EDB or BDE
B
A
C
D
E
4 ACTIVITY SHEET
Teacher’s Copy
LESSON 106: Orthogonal projection of a line on a plane.
1. The figure shows a triangular prism PQRSTU. Draw and name the orthogonal projection of each of the following lines on the plane PQRS.
T
P
Q
R
S
U
M
N
a)
TQ
b)
QU
T
M
Q
U
MQ
or
QM
NQ
or
QN
2. The figure shows a cube ABCDEFGH. Based on the diagram given, complete the table below.
Line Plane Orthogonal
Projection
Angle between line and plane
1 AG ABCD AC GAC
2 HB ABEF BF HBF
3 CH EFGH HG CHG
4 EG DCHG HG EGH
5 HB BCFG FB HBF
A
B
C
D
E
F
6
3. The figure shows a pyramid ABCDEFG. Based from diagram given, complete the table below.
No Line Plane Angle between line and plane
1 EF ABCD EFG or GFE
2 EA ABCD EAC or CAE
3 EB ABCD EBD or DBE
4 EG ABCD EGF or FGE
5 ED ABCD EDB or BDE
B
A
C
D
E
ACTIVITY SHEET
Pupil’s Copy
LESSON 107: Problems Solving on Angle between a Line and a Plane.
The diagram shows a cuboid. KG = 2HK. DL = HK. By sketching an appropriate right-angled triangle, find the following:
(a) the length of FD.
(b) the length of KA.
(c) the angle between FD and BCGF.
(d) the angle between KA and EFGH.
A B
D
E F
G H
C
9 cm
4 cm
6 cm K
2 ACTIVITY SHEET
Teacher’s Copy
LESSON 107: Problems Solving on Angle between a Line and a Plane.
The diagram shows a cuboid. KG = 2HK. DL = HK. By sketching an appropriate right-angled triangle, find the following:
(a) the length of FD.
2
2 BD
BF
FD= +
= 42+(AB2+AD2)
= 16+92+62
= 133 = 11.53 cm
(b) the length of KA.
2 2
AL KL KA= +
42 ( 2 2)
DL AD +
+ =
= 16+62+32 = 7.81 cm
(c) the angle between FD and BCGF.
The orthogonal projection of FD on BCGF is FC.
So, the angle between FD and BCGF is ∠CFD.
DF CD CFD= ∠ sin 53 . 11 9 = = 0.7806
∠CFD = 51.32° or 51° 19'
(d) the angle between KA and EFGH.
The orthogona l projection of KA on EFGH is KE.
So, the angle between KA and EFGH is ∠EKA.
AK AE EKA= ∠ sin 81 . 7 4 = = 0.5122
∠EKA = 30.81° or 30° 49'
A B D E F G H C 9 cm 4 cm 6 cm K F
D B
K
A L
L
F
D C
11.53 cm 9 cm
A
E K
ACTIVITY SHEET Pupil’s Copy
Lesson 108: Line of Intersection between Two Planes.
Plane A Plane B Line of intersection
EDIJ DCHI
BFIC ABGF
AGH BCHG
ABCDE DEJI
DCG BCHG
Plane A Plane B Line of intersection Pair of lines perpendicular to line of intersection
ABCD BCFE
AFE BCFE
B
G H I
J
E
A D
F
C
Based on figure given above, state the line of intersection between the following planes: Question 1
A
B E F
C D
Question 2
2
Plane A Plane B Line of intersection Pair of lines perpendicular to line of intersection
AFC ABCD
BEF BCE
BDF ABCD
Plane A Plane B Line of intersection Pair of lines perpendicular to line of intersection
AEGC ABFE
BHD ADHE
EFGH ABFE Question 3
A B
C D
F
E
Based on figure given above, state the line of intersection between the following planes and the pair of lines perpendicular to the line of intersection.
Question 4
Based on figure given above, state the line of intersection between the following planes and the pair of lines perpendicular to the line of intersection
A B
F E
C G H
Teacher’s Copy
Lesson 108: Line of Intersection between Two Planes.
Plane A Plane B Line of intersection
EDIJ DCHI Line DI
BFIC ABGF Line BF
AGH BCHG Line GH
ABCDE DEJI Line ED
DCG BCHG Line CG
Plane A Plane B Line of intersection Pair of lines perpendicular to line of intersection
ABCD BCFE Line BC Line AB & Line BE or Line CD & Line CF
AFE BCFE Line EF Line EA & Line EB
BED ABE Line BE Line EA & Line ED B
G H I
J
E
A D
F
C
Based on figure given above, state the line of intersection between the following planes: Question 1
A
B E F
C D
Question 2
4
Plane A Plane B Line of intersection Pair of lines perpendicular to line of intersection
AFC ABCD Line AC Line EF & Line BD
BEF BCE Line BE Line EC & Line EF
BDF ABCD Line BD Line EF & Line AC
Plane A Plane B Line of intersection Pair of lines perpendicular to line of intersection
AEGC ABFE Line AE Line EF & Line EH or Line AB & Line AD
BHD ADHE Line DH Line AD & Line BD
EFGH ABFE Line EF Line EA & Eh or Line FB & Line FG Question 3
A B
C D
F
E
Based on figure given above, state the line of intersection between the following planes and the pair of lines perpendicular to the line of intersection.
Question 4
Based on figure given above, state the line of intersection between the following planes and the pair of lines perpendicular to the line of intersection
A B
F E
C G H
ACTIVITY SHEET Pupil’s Copy
LESSON 109: Angle between Two Planes.
1. Based on the diagram given, identify the angle between the two planes given by completing the table below.
No Plane Plane Angle between two p lanes
1 UON MNPQ
2 ROQ MNPQ
3 NORQ MORP
4 RSU MORP
5 TQU NORQ
M
N
O
P
Q
R
S
T
2
2. The figure shows a cuboid ABCDPQRS. Complete the table given in order to identify the the angle between two planes.
No Plane Plane Angle between two planes
1 CDS ABCD
2 PQB PQRS
3 ABC ABPQ
4 SRP DCSR
5 ABPQ CBRQ
Q
P
R
S
B
A
complete the table below.
No Plane Plane Angle between two planes
1 ABCD EFG or GFE
2 ABCD EGF or FGE
3 ABCD EHI or IHE
4 ABCD EIH or HIE
B
A
C
D
E
F
G
4 ACTIVITY SHEET
Teacher’s Copy
LESSON 109: Angle between Two Planes.
1. Based on the diagram given, identify the angle between the two planes given by completing the table below.
No Plane Plane Angle between two planes
1 UON MNPQ ONM or MNO
2 ROQ MNPQ RQP or PQR
3 NORQ MORP UST or TSU, NOM or MON, QRP or PRQ
4 RSU MORP UST or TSU
5 TQU NORQ SUT or TUS
M
N
O
P
Q
R
S
T
2. The figure shows a cuboid ABCDPQRS. Complete the table given in order to identify the the angle between two planes.
No Plane Plane Angle between two planes
1 CDS ABCD SDA or ADS
2 PQB PQRS RQB or BQR
3 ABC ABPQ CBQ or QBC
4 SRP DCSR DSP or PSD
5 ABPQ CBRQ RQP or PQR, CBA or ABC
Q
P
R
S
B
A
6
3. The figure shows a pyramid ABCDEFG. Based from diagram given, complete the table below.
No plane Plane Angle between two planes
1 EAB ABCD EFG or GFE
2 ECD ABCD EGF or FGE
3 EAD ABCD EHI or IHE
4 ECB ABCD EIH or HIE
B
A
C
D
E
F
G
ACTIVITY SHEET Pupil’s Copy
Lesson 110: Problems Solving on Lines and Planes in 3-Dimensional Shapes.
The figure shows two wooden blocks attached together. Based on the figure, solve the questions given:
Question 1
Question 2
The figure shows a prism. M and N are the midpoints of AB and DE respectively.
A B
C
D K
J
M
N L
G I
F E
H
15cm 40cm
50cm 55cm
20cm
1. What is the length of the diagonal DI?
2. Determine the angle between planes ILNK and CILG.
3. Determine the angle between horizontal plane DCGH and the diagonal DF.
4. Determine the angle between planes LGKJ and CGFB.
A B
B
M
E N
F
D
16cm
16cm 8cm
1. What is the length of the diagonal AE?
2. Identify the angle between planes ACFD and ABED.
2 ACTIVITY SHEET
Teacher’s Copy
Lesson 110: Problems Solving on Lines and Planes in 3-Dimensional Shapes.
The figure shows two wooden blocks attached together. Based on the figure, solve the questions given:
Question 1
Question 2
The figure shows a prism. M and N are the midpoints of AB and DE respectively.
A B
C
D K
J M N L G I F E H 15cm 40cm 50cm 55cm 20cm
1. What is the length of the diagonal DI?
2. Determine the angle between planes ILNK and CILG.
3. Determine the angle between horizontal plane DCGH and the diagonal DF.
4. Determine the angle between planes LGKJ and CGFB.
25cm
69.44°
42.0°
36.02°
A B
B M E N F D 16cm 16cm 8cm
1. What is the length of the diagonal AE?
2. Identify the angle between planes ACFD and ABED.
3. Determine the angle between the diagonal BF and the plane ABED.
18.87cm
58.0°
