ACTIVITY SHEET Pupil’s Copy Lesson 104: Horizontal Planes, Vertical Planes and Inclined Planes. - Chapter 11 Line and Planes in 3 dimension

  Mathematics Form 4 ACTIVITY SHEET Pupil’s Copy

Lesson 104: Horizontal Planes, Vertical Planes and Inclined Planes.

  J

  Question 1

  I E F H D C A G B

  Based on the figure given above, identify the type of planes for: Plane Type of planes

  EDIJ ABGF BGHC ABCDE CHID

  F

  Question 2

  C D E B A

  

Based on the figure given above, identify the type of planes for:

Plane Type of planes

  ABCD AEB BCFE

  Mathematics Form 4 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:

Based on the figure given above, identify the type of planes for:

  Mathematics Form 4 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 AEB Horizontal 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

Based on the figure given above, identify the type of planes for:

  Mathematics Form 4 BCFE Vertical plane

  F

  Question 3

  D C E A B

  

Based on the figure given above, identify the type of planes for:

Plane Type of planes

  AFB Inclined plane CFD Inclined plane ABCD Horizontal plane

  Question 4

  H G F E D C A B

  

Based on the figure given above, identify the type of planes for:

Plane Type of planes

  ABFE Vertical plane EFGH Horizontal plane ABCD Horizontal plane

  Mathematics Form 4 ACTIVITY SHEET Pupils’ Copy Lesson 105: Lines on a Plane, Lines Intersect with a Plane and Normals.

  1. Name all the lines that lie on the plane CDHG.

  Question 1 Answer:

  F G 2. Name all the lines that intersect with the plane BCGF.

  H E

  Answer :

  B C

  3. Name all the normals to the plane ABFE

  D A

  Answer : 1. Name all the lines that lie on the plane RQTU. Question 2

  S U

  Answer:

  W R P 2. Name all the lines that intersect with the plane PQTS.

  Answer :

  T

  3. Name all the normals to the plane STU

  V Answer : Q 1. Name all the lines that lie on the plane ABHG.

  Question 3

  K J

  Answer:

  E D 2. Name all the lines that intersect with the plane FAGL.

  L

  I Answer : F C G H

  3. Name all the normals to the plane ABCDEF

  A B

  Answer : 1. Name all the lines that lie on the plane ABCD. Question 4

  C G

  Answer:

  D H O K 2. Name all the lines that intersect with the plane LKOP.

  L P

  Answer :

  J N

  I B M F

  3. Name all the normals to the plane EFGH

  E A

  Answer :

  Mathematics Form 4 ACTIVITY SHEET Teacher’s Copy Lesson 105: Lines on a Plane, Lines Intersect with a Plane and Normals.

  1. Name all the lines that lie on the plane CDHG.

  Question 1 Answer: Line: CD, DH, HG, GC, DG

  F G 2. Name all the lines that intersect with the plane BCGF.

  H E

  Line: BA, CD, GH, FE, GD Answer :

  B C

  3. Name all the normals to the plane ABFE

  D A

  Line: AD, BC, FG, EH Answer : 1. Name all the lines that lie on the plane RQTU.

  Question 2

  S U

  Answer:

  W Line: RQ, QT, TU, UR, WV R P 2. Name all the lines that intersect with the plane PQTS.

  Line: QR, VW, TU, PR, SU Answer :

  T

  3. Name all the normals to the plane STU

  V Line: SP, UR, TQ

  Answer :

  Q 1. Name all the lines that lie on the plane ABHG.

  Question 3

  K J

  Answer: Line: AB, BH, HG, GA

  E D 2. Name all the lines that intersect with the plane FAGL.

  L

  I Line: AB, GH, LK, FE

  Answer :

  F C G H

  3. Name all the normals to the plane ABCDEF

  A B

  Line: AG, BH, CI, DJ, EK, FL Answer : 1. Name all the lines that lie on the plane ABCD.

  Question 4

  C G

  Answer: Line: AB, BC, CD, DA, IJ, JK, KL, LI

  D H O K 2. Name all the lines that intersect with the plane LKOP.

  L P

  Line: LI, KJ, PM, ON Answer :

  J N

  I B M

  3. Name all the normals to the plane EFGH

  F E A

  Line: EA, FB, GC, HD Answer :

  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.

  U S T R N P M Q

  a) TQ

  b) QU

2. The figure shows a cube ABCDEFGH. Based on the diagram given, complete the table below.

  H G E F D C A B Line Plane Orthogonal Angle between line Projection and plane

  1 AG ABCD HB ABEF

  2 CH EFGH

  3 EG DCHG

  4 HB BCFG

  5

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 F G

  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.

  U S T R N P M Q T Q M

  a) TQ MQ or QM U Q N NQ

b) QU or QN

2. The figure shows a cube ABCDEFGH. Based on the diagram given, complete the table below.

  H G E F D C A B Line Plane Orthogonal Angle between line Projection and plane

AG ABCD AC GAC

  1 HB ABEF BF HBF

  2 CH EFGH HG CHG

  3

  

4 EG DCHG HG EGH

  

5 HB BCFG FB HBF

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 F G

  ACTIVITY SHEET Pupil’s Copy LESSON 107: Problems Solving on Angle between a Line and a Plane.

  The diagram shows a cuboid. KG = 2 HK .

  = . By sketching an appropriate

DL HK

  H K G right-angled triangle, find the following:

  4 cm (a) the length of .

  FD F E L D C

  6 cm

  A B

  9 cm (b) the length of KA .

  (c) the angle between FD and BCGF .

  (d) the angle between KA and EFGH .

  ACTIVITY SHEET Teacher’s Copy

LESSON 107: Problems Solving on Angle between a Line and a Plane.

  The diagram shows a cuboid. KG = 2 HK . DL K

  = HK . By sketching an appropriate right- H G angled triangle, find the following:

  4 cm (a) the length of .

  FD F E L D C ^{2 2}

  = _{2 2 2}

• FD BF BD

  6 cm

AB AD

  = 4 ( ) + + A B

  9 cm ^{2 2 F}

  16

  9

  6 =

  133 =

   = 11.53 cm B D (b) the length of KA . ^{2 2}

KA KL AL

  = _{2 2 2} 4 ( AD DL )

• K

  = + + _{2 2} A = 16 + +

  6

3 L

  = 7.81 cm (c) the angle between FD and BCGF .

  FD BCGF FC The orthogonal projection of on is . FD BCGF CFD So, the angle between and is .

  ∠

  9 cm

  D C CD CFD sin ∠ =

  DF

  11.53 cm

  9 =

  F 11 .

  53 = 0.7806

  CFD = 51.32 or 51 19'

  ∠ ° ° (d) the angle between KA and EFGH.

  KA EFGH KE The orthogona l projection of on is . KA EFGH EKA So, the angle between and is .

  ∠ AE EKA sin ∠ =

  K E AK

  4

  4 cm

  =

  7.81 cm 7 .

81 A

   = 0.5122 EKA

   = 30.81 or 30 49' ∠ ° °

  Mathematics Form 4 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 BED ABE

  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 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.

  Mathematics Form 4

  F

  Question 3

  D C E A B

  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.

  Pair of lines perpendicular to line of Plane A Plane B Line of intersection intersection AFC ABCD BEF BCE BDF ABCD Question 4

  H G F E C D A B

  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 Pair of lines perpendicular to line of Plane A Plane B Line of intersection intersection

  AEGC ABFE BHD ADHE EFGH ABFE

  Mathematics Form 4 ACTIVITY SHEET 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 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.

  Mathematics Form 4

  F

  Question 3

  D C E A B

  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.

  Pair of lines perpendicular to line of Plane A Plane B Line of intersection 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 Question 4

  H G F E C D A B

  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 Pair of lines perpendicular to line of Plane A Plane B Line of intersection 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

  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 U

2. The figure shows a cuboid ABCDPQRS. Complete the table given in order to identify the the angle between two planes.

  D C R S A B

Q

P

No Plane Plane Angle between two planes

CDS ABCD

  1

  2 PQB PQRS

  3 ABC ABPQ

  4 SRP DCSR

  5 ABPQ CBRQ

3. The figure shows a pyramid ABCDEFG. Based from diagram given, 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 H

  I

  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 U

2. The figure shows a cuboid ABCDPQRS. Complete the table given in order to identify the the angle between two planes.

  D C R S A B

Q

P

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 SRP DCSR DSP or PSD

  4 ABPQ CBRQ RQP or PQR, CBA or ABC

  5

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 H

  I

  Mathematics Form 4 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.

   3. Determine the angle between the diagonal BF and the plane ABED.

  Mathematics Form 4 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° 25.52°