OLEH

PN. CHUANG BEE ENG

SM TEKNIK BATU PAHAT

AB

CD

E F

GH

PLANE AT THE TOP : PLANE EFGH

ACTIVITY 1 : TO IDENTIFY THE PLANE

AB

CD

E F

GH

PLANE ON THE LEFT : PLANE ADHE

AB

CD

E F

GH

PLANE IN THE FRONT : PLANE ABFE

AB

CD

E F

GH

PLANE AT THE BACK : PLANE DCGH

AB

CD

E F

GH

PLANE AT THE BOTTOM: PLANE ABCD

AB

CD

E F

GH

PLANE ON THE RIGHT : PLANE BCGF

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

AT THE BOTTOM OF ….

ON THE TOP OF ….

AT THE BACK OF ….

IN FRONT OF ….

TO THE LEFT OF ….

TO THE RIGHT OF ….

ACTIVITY 2 : TO DETERMINE THE LOCATION OF A POINT

A B

CD

EF

GH

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

ANGLE BETWEEN A LINE AND A PLANE

A

BC

LINE

PLANE

BA

CD

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.

BA

CD

E F

H G

ACTIVITY 3 : To Identify The Angle Between A Line And A Plane

AG 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.

EXAMPLE 1(b)

BA

CDE

H G

F

Diagram 1(b)

Diagram 1b shows a cuboid ABCDEFGH. Name the angle between the line HB and the plane ABCD.

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

BA

CD

E

H G

F

4cm

12cm

Diagram 2a

5cm

Draw the line AH and shade the plan DCGH in diagram 2a.

1.

SolutionsStepsNo

A

CD

E

H G

F

5cm

4cm

12cm

BDiagram 2a

Diagram 2a shows a cuboid, ABCDEFG. Find the angle between the line AH and the plane DCGH.

No Steeps Solutions

2 Use the method you have learned in activity 3, identify the angle between the line AH and the plane DCGH

HA

back

D

5cm

BA

CDE

H G

F

4cm

12cm

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

DA

5cm

4cm

A H D

BA

CDE

H G

F

12cm

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

DA

5 cm

4 cm

5cm

BA

CDE

H G

F

4cm

12cm

No Steps Solutions

6 Mark,- the opposite side, AD asT- the adjacent side, HD as S

H

DA

5 cm

4 cm

S

T

5cm

BA

CDE

H G

F

4cm

12cm

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’

– TOAA

O T

- SOH

H

O S

– CAHH

A C

5

4

5

4

5cm

BA

CD

E

H G

F

4cm

12cm

example 2 (b)

Diagram 2b shows a cuboid,ABCDEFGH. Calculate the angle between the line HB and the plane BCGF

A B

CD

E F

GH

4 cm

12 cm

3 cm

Diagram 2b

ANGLE BETWEEN TWO PLANES

ACTIVITY 5 : To Identified The Angle Between Two Planes

A

E

B

CD

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)

BA

CDE

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

BA

CDE

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

BA

CDE

H G

F

Diagram 3a

AH / 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

BA

CDE

H G

F

Diagram 3a

AH/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

BA

CDE

H G

F

Diagram 3a

AH

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

BA

CDE

H G

F

Diagram 3a

AH

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

BA

CDE

HG

F

Diagram 3a

Bottom

AH 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

EXAMPLE 3(b)

Diagram 3b

E5cm

BA

CD

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

THANK YOU