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MATHEMATICS

FORM 4

LEARNING AREA : LINES AND PLANES IN 3-DIMENSIONS

LEARNING OBJECTIVE:

Pupils will be taught to

understand and use the concept of angle betweenlines and planes to solve problems.

LEARNING OUTCOME:Pupils will be able to

determine the angle between a line and a plane.

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SURVIVAL

A B C D E

What direction should the

runner take?

OA, OB, OC, OD or OE

O

WHY ???

OC is the

shortest distance.

Safe region

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SET INDUCTION

LINES AND PLANES IN 3-DIMENSIONS

State the shortest distance

A B

CD

G

FE

H

(b) from F to plane(i) ABCD

(ii) ADHE

(iii) CDHG

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SET INDUCTION

LINES AND PLANES IN 3-DIMENSIONS

State the shortest distance

A B

CD

G

FE

H

(c) from G to plane(i) ABCD

(ii) ABFE

(iii) ADHE

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SET INDUCTION

LINES AND PLANES IN 3-DIMENSIONS

State the shortest distance

A B

CD

G

FE

H

(d) from D to plane(i) EFGH

(ii) ABFE

(iii) BCGF

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SET INDUCTION

LINES AND PLANES IN 3-DIMENSIONS

State the shortest distance

A B

CD

G

FE

H

(e) from C to plane(i) EFGH

(ii) ADHE

(iii) ABFE

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MODELOFBOX

RULER

ANGLEBETWEENLINE (RULER)ANDBASEOFBOX (PLANE)

SET INDUCTION III

LINES AND PLANES IN 3-DIMENSIONS

Show the angle between line and plane

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MODELOFBOX

RULER

ANGLEBETWEENLINE (RULER)ANDBASEOFBOX (PLANE)

SET INDUCTION III

LINES AND PLANES IN 3-DIMENSIONS

Show the angle between line and plane

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A B

CD

E F

GH

Plane Line Position

of plane

ABCD

Letter(on line

EC) not

touching the

plane

Letter(on line

EC) that

touches the

plane

Nearest

distance

to plane

Name

of angle

ABCD EC

Name the angle between the line EC and the plane ABCD

bottom EC A ECA

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A B

CD

E F

GH

Plane Line Position

of plane

EFGH

Letter (on

line EC) not

touching theplane

Letter (on

line EC) that

touches theplane

Nearest

distance

to plane

Name

of

angle

EFGH EC

Name the angle between the line EC and the plane EFGH

topC E G CEG

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A B

CD

EF

GH

Plane Line Position

of plane

Letter (on

line EC) not

touching theplane

Letter (on

line EC) that

touches theplane

Nearest

distance

to plane

Name

of

angle

BCGF JB

J is the midpoint ofEH and L is the midpoint of FG.Name the angle between the line JB and the plane BCGF

rightJ B L JBL

K

J L

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A B

CD

EF

GH

Plane Line Position

of plane

Letter not

touching

the plane

Letter that

touches the

plane

Nearest

distance

to plane

Name

of

angle

ABFE JB

J is the midpoint ofEH.

Name the angle between the line JB and the plane ABFE

front J B E JBE

J

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A B

CD

E F

GH

1. EA is the . from point

E to plane ABCD.

normal

2.AC is the ofEC on

plane ABCD.

orthogonal projection