THREE DIMENSIONS

Basic Competence : Determine state of distance and angle which related point, line and plane on the space three dimensions

Indicators

• Student able to determine state line with line on space three dimensions

• Student able to determine state line with plane on three dimensions

SSTATE Point, line, and plane TATE Point, line, and plane

ON SPACEON SPACE

A. state Point with line

B. state Point with plane

C. state line with line otherther

D.D. state line with planestate line with plane

I. Definition

II. state Point, line, and plane

A. Point

B. line

C. plane

D. Aksioma line and plane

A. PointA. Point

AA P

(a) Point A (b) Point P

Definition

• a Point drawed with use sign dot.• name a Point usually use capital letters A, B,

C, P, Q, or R

B. line

g

A

(a) line g (b) Segment line AB

D E F I N I TION• a line define with length of light.

• part from a line called segment line.• name from a line using a little alphabet / name

segment can look at picture above.

B

C. planeC. plane(a) plane (a) plane αα

α

(b) plane (b) plane ABCDABCD

A B

D C

(c) plane (c) plane ββ

β

(e) plane (e) plane KLMNKLMN

K L

N M

AKSIOMA I

Passing through two point can only be drawn one straight line.

A

B

g

State point with line

Point A located on line g

A

g

•Point B out side with line h

Bh

α

state Point with planestate Point with planePoint A located on plane Point A located on plane αα

A

Point B out side with plane Point B out side with plane ββ

B

β

α

state line with others linestate line with others line

A

A. line g and h concurrent in point A

g

h

B. line g and h close up

α g

h

α

C. line g and h paralel

D. line g and h crossed

α

gh

g

h

line perpendiculer with plane

A line (g)perpendiculer with a two line (k & l),

line k and l concurrent

then line g perpendiculer with plane v

g

V

k

l

g k, g l,

k and l concurrent, so g V

line perpendiculer with plane

V

g

ab

A line g perpendiculer with plane v

then, line g perpendiculer with all line on plane v

g a, g b,

A BCD

HE F

G

EXAMPLE

Shows that line AE perpendiculer with Plane ABCD.

Prove :

line AE ┴ AD

line AE ┴ AB

AD and AB concurrent, AB & AD on

plane ABCD

Then, AE ┴ Plane ABCD

Characterictic on cube

1. If one from two line paralel, perpendiculer on a plane then line other perpendiculer with that plane too

2. If two line perpendiculer with a plane, then that lines paralel

3. Through a point out side for line, only can form one plane which perpendiculer which that line.

A BCD

HE F

G

EXAMPLE

Shows that line AE // line DH

Prove :

line AE ┴ ABCD

line DH ┴ AD

line DH ┴ CD

Ad and CD concurrent and located on plane ABCD

DH ┴ ABCD

, AE ┴ Plane ABCD

DH ┴ plane ABCDSo, AE // DH

Exercises

Knowing Cube ABCD EFGH, with aksioma or characteristic show that’s

1. AB ADHE┴2.AB CG┴3. AB // GH4. AC DF┴5. AG BDE┴6. AG CFE┴

THANKS

SEE YOU NEXT TIME

D. D. AKSIOMA line and AKSIOMA line and planeplane

In geometry an three important aksioma. (Euclides, mathematicians In geometry an three important aksioma. (Euclides, mathematicians drom Alexandria)drom Alexandria)

AKSIOMA I

AKSIOMA III

AKSIOMA IIEuclidesEuclides

AKSIOMA IIAKSIOMA IIif a line and a plane have two common Point, if a line and a plane have two common Point, then all point on line located on planethen all point on line located on plane

A B

α

AKSIOMA IIIAKSIOMA III

Passing through three point can form only one Passing through three point can form only one planeplane

A

C

αB