5 Waja 2010 f4 Teachers Copy Lines Planes

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Program WAJA Negeri Perak Tahun 2010

FORM 4 MATHEMATICS Module 5 : Page 1

Learning Area 11: LINES AND PLANES IN 3 DIMENSIONS Worksheet 1.1

Learning Objective 11.1: Uner!tan an u!e the conce"t o# ang$e bet%een $ine! an "$ane! to

!o$ve "rob$em!.

Learning Outcome &ii' (enti#) hori*onta$ "$ane!+ vertica$ "$ane! an inc$ine "$ane!.

Activity 1:Determine base, horizontal planes, vertical planes and inclined planes.

,o$i -a!e ori*onta$

"$ane

/ertica$

"$ane

(nc$ine

"$ane

1

P, P, P,UT+

PT+

U,

TU

2

A-3 A-3 4

/-+

/3A+

/A-5

/3

6

P, P,+

TU/W

UP/+

T,W+

/W+

UP,T

4

7

P, P,

U/+

TP,W+

TPU+

W,/

TU/W

8

A-3 A-3 /3

/A3

/A-+

/-

Teachers copy

A B

C

V

3


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Activity 3 :denti!y and name the normal and orthogonal pro"ection o! a line #V on the plane #$%&

in each o! the !ollowing ob"ects

,o$i Norma$ Orthogona$ Projection

1.

/, ,P

2.

/ P

6.

/ P

7.

/, ,P

Teachers copy


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,o$i Norma$ Orthogona$ Projection

8.

/ P

9.

/ P

.

/O PO

;.

/ P

Teachers copy


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Learning Area 11 :LINES AND PLANES IN 3 DIMENSIONS Worksheet 3.1

Learning Objective 11.1: Uner!tan an u!e the conce"t o# ang$e bet%een $ine! an "$ane! to !o$ve

"rob$em!.

Learning Outcome &viii' 3etermine the ang$e bet%een a $ine an a "$ane.

Activity 1 :Determine the angle between a line and a plane.

,o$i Norma$ Orthogona$

Projection

ight4 ang$e triang$e Name the

ang$e

1.

Line P/ an P$ane P,

/ P /P

2.

Line W an P$ane P,

W

W

6.

Line U an P$ane P,

UP P

UP

Teachers copy

P

/

P

U

W


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Projection

ight4 ang$e triang$e Name the ang$e

7.

Line PT an P$ane P,

T, ,P

TP,

8.

Line PW an P$ane P,

W P

WP

9.

Line U an P$ane P,

UP P

UP

.

Line T< an P$ane J


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FORM 4 MATHEMATICS Module 5 : Page


Projection

ight4 ang$e triang$e Name the ang$e

>.

Line P< an P$ane J


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FORM 4 MATHEMATICS Module 5 : Page 1%

2. (enti#) the $ine o# inter!ection bet%een the t%o given "$ane!:

i.

&a' P$aneABCDan "$aneBC

i' ommon vertice!: @@@an @@@

ii' Line o# inter!ection: @@@@@@..

&b' P$aneABCDan "$aneAD



&c' P$aneADan "$aneAB



ii.

&a' P$aneABCan "$aneACD



&b' P$aneBCDan "$aneABD



&c' P$aneADCan "$aneABD



iii.

&a' P$ane VABan "$ane ABCD



&b' P$ane VBCan "$aneABCD



&c' P$ane VBDan "$aneABCD



Teachers copy

A

A

B C

D

V

D

AB

C

D

B

# C

#C

A D

AD

A E

AE

A C

AC

# D

#D

A D

AD

A #

A#

# C

#C

# D

#D

C

O


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Learning Area11: LINES AND PLANES IN 3"DIMENSIONS Worksheet 6.1

Learning Objective 11.2: Uner!tan an u!e the conce"t o# ang$e bet%een t%o "$ane! to !o$ve

"rob$em!.

Learning Outcome &ii' 3ra% a $ine on each "$ane %hich i! "er"enicu$ar to the $ine o# inter!ection

o# the t%o "$ane! at a "oint on the $ine o# inter!ection.

Activity 1: Thining &mart

3ra% t%o !traight $ine!+ one on each "$ane! !tate+ %hich are "er"enicu$ar to the $ine o# inter!ection

o# the t%o "$ane! at the "oint given./0o( may wor in pairs i! necessary1

E&a'(le:

The "$ane2&%3%ith the "$ane4532at

"oint3.

&a' The "$ane#42& %ith the "$ane4532

at "oint4.

,tate:

i' Line o# inter!ection: @@@@@..

ii' Line %hich i! "er"enicu$ar to the

$ine o# inter!ection at "oint =:@@@@.@ an @@@@@@

,tate:



$ine o# inter!ection at "oint4: @@@@.@ an @@@@@@

3ra% the $ine! a! !tate above: 3ra% the $ine! a! !tate above:

Teachers copy

& %

2 3

4 5

NM

LM RM

4

&

#

23

5

3

%

54

$

2

&

#

& %

2 3

4 5

#

2

4

3

5

&

)N

P) )L


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&b' The "$ane#$%& %ith the "$ane53%$

at "oint%.

&c' The "$ane42%$%ith the "$ane 53%

at "oint $.

,tate:



$ine o# inter!ection at "oint%:

@@@@.@ an @@@@@@

,tate:



$ine o# inter!ection at "oint $:

@@@@.@ an @@@@@@

3ra% the $ine! a! !tate above: 3ra% the $ine! a! !tate above:

Teachers copy

# $

%&

5

3

5

# $

%&

3

5

$

2 3

%

4

4

*R

SR RM

*R

)* *L

%

$

2 3

5


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Activity 2:Do yo( now how to draw6

3ra% the "air o# $ine! "er"enicu$ar to the $ine o# inter!ection #or each o# the "air! o# "$ane! given

be$o%:

1

.

&a'AD)an')

2

.

&b' CDanAD

6.

&a'#78anABCD.

Teachers copy

D

#

B

A C

D

'

)

C

B

D

A

C

D

A

B

#

A

C

78

C

9

0

:

A

)

'

D

A

B

78

D

C

9

0

:


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Learning Area11: LINES AND PLANES IN 3"DIMENSIONS Worksheet 7.1

Learning Objective 11.2: Uner!tan an u!e the conce"t o# ang$e bet%een t%o "$ane! to !o$ve

"rob$em!.

Learning Outcome &iv' ,o$ve "rob$em! invo$ving $ine! an "$ane! in 64imen!iona$ !ha"e!.

STEPS TO FOLLO,:

S-e( 1: S.e-/0 -0e 0a(e eeg -o -0e o'a-o g8e9

S-e( 2: a; Ide- -0e le o -ee/-o e-


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$uded E&e/e:

$udedSolu-o:

&a' U!ing P)thagora!5 Theorem+D? 12 cm+'? 18 cm

) ? 22 18; +

< @@@@@..

&b' S-e( 1: S-e( 2:

(enti#) the ang$e bet%een the t%o "$ane!

&)anD')'

@@@@@

S-e( 3: S-e( 4:

,ketch the right ang$e triang$e U!ing Trigonometr) atio to

in &tep +. ca$cu$ate the an!%er.

Teachers copy

cm

The #igure !ho%! a right "ri!m %ith a

uni#orm tra"e*iumDa! it! cro!! !ection.a$cu$ate:

&a' the $ength o#)+

&b' the ang$e bet%een the "$ane!

)anD').

= cm

*> cm

)

)

cm

'

'

D

1 cm

D,

D

tanD ?;

12

? 1.8

D < >=.@+oor >=o*E

D

D,

) 4

* cm

'

E cm

D *+ cm


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No-e:

1.Letter! $abe$$e in the iagram given are ca$$e vertice!.

The $ine o# inter!ection o# t%o "$ane! i! the $ine joining the common vertice! in the t%o

"$ane!.

2.T%o "$ane! inter!ect at a !traight $ine. The !traight $ine i! ca$$e the $ine o# inter!ection

o# the t%o "$ane!.

6.

7.

Teachers copy

A 2 B

D 3 C Line o# inter!ection i!7:0.

Line! "er"enicu$ar to7:0

are7D an7A, :3 an:2

or 0Can 0B.7 : 0

D 3 C

A 2 B

7 : 0

The ang$e bet%een the

$ine! "er"enicu$ar to the

$ine o# inter!ection o# t%o

"$ane! i! the ang$e

bet%een the t%o "$ane!.

Line!

"er"enicu$ar

to the $ine o#

inter!ection

Line o#

inter!ection

#lane +

#lane *

line ofintersection

5 Waja 2010 f4 Teachers Copy Lines Planes

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