This document defines and describes the positions of points, lines, and planes in three-dimensional space according to several axioms and definitions. It defines a point, line, and plane and the possible positions of each in relation to one another, such as a point being on or off a line, two lines intersecting or being parallel, and a plane intersecting or being parallel to another plane or line. The document provides examples to illustrate each type of position between the geometric elements in three dimensions.

1. Three-Dimensional
objecT

2. Created By:
1. Dina Ratnasari
2. Meiga Suraidha
3. Kristalina Kismadewi
4. Chairul Muhafidlin
5. Kiky Ardiana

3. Position of Point, Line, and
Plane in Polyhedral
1. The Definition of Point, Line, and Plane
2. Axioms of Line and Plane
3. Position of a Point toward a Line
5. Positions of a Line toward Other Lines
7. Positions of a Plane to Other Planes
4. Position of a Point toward a Plane
6. Positions of a Line toward a Plane

4. A
.
Point A
a. Point
The Definition of Point, Line,
and Plane
A point is determined by its position and does have
value. A point is notated as a dot and an uppercase
alphabet such as A,B,C and so on.
B
.
Point B

5. b. Line
A line is a set of unlimited series of points. A line is
usually drawn with ends and called a segment of
line (or just segment) and notated in a lowercase
alphabet, for examples, line g,h,l. A segment is
commonly notated by its end points, for examples,
segment AB,PQ.
line g segment AB
A B
••

6. C. Plane
A plane is defined as a set of points that have
length and area, therefore planes are called two-
dimentional objects. A plane is notated using
symbols like α, β, γ, or its vertexes.
Plane α
A
CD
B
Plane ABCD
α

7. Axioms of Line and Plane
Axioms is a statement that is accepted as true without
further proof or argument. The following are several
axioms about point, line, and plane.
B
A straight line that is drawn
through two points
A
α
A line that is drawn on a
plane
A B
Three different points on plane
•A
•C
•B
α
••
••
α
A
g
h
Two parallel lines on the same
plane

8. Position of a Point toward a Line
There are two possible positions of a point toward
a line, which are the point is either on the line or
outside the line.
a. A point on a line
b. A point outside a line
a point is stated on a line if the point is passed by
the line.
Point A is on line g
•
A
a point is outside a line if the point is not passed
through by the line.
g
g•A
Point A is outside line g

9. Position of a Point toward a
Plane
a. A Point on a plane
A point is on a plane if the point is passed by the plane
A point is outside a plane if the point is not passed
by the plane.
b. A point outside a plane
AA
•
v Point A is on plane V
v Point A is outside plane V

10. Positions of a Line toward other
Lines
a. Two lines intersect Each Other
Two lines intersect each other if these lines are
on a plane and have a point of intersection
b. Two parallel lines
Two lines are parallel if these lines are on a
plane and do not have a point
hP
g
V Line G intersect line h
V
h
g

11. c. Two lines cross over
Two lines cross over each other if these lines are
not on the same plane or cannot form a plane
V
W
h
g
Line g crosses over line h

12. Positions of a Line toward a
Plane
The positions of a line toward a plane may be the
line is on the plane, the line is parallel to the plane or
the line intersects (cuts) the plane.
a. A line on a plane
A line is on a plane if the line and the plane have at
least two points of intersection
A B• •• g
V
•
Line g is on plane V

13. b. A line parallel to a plane
c. A line intersects a plane
A line is parallel to a plane if they do not have any
point of intersection
A line intersects a plane if they have at least a
point of intersection
V Line g is parallel to plane V
g
V Line g is intersects plane V
g
•A

14. Positions of a Plane to Other
Planes
Positions between two planes may be parallel, one
is on the other or intersecting.
a. Two parallel planes
Planes V and W are parallel if these planes do not
have any point of intersection
V
W
Two parallel planes

15. b. A plane is on the other plane
Plane V and W are on each other if every point on V
is also on W, or vice versa
VW Two planes are on each other
c. Two Intersecting Planes
Plane V and W intersect each other if they have exactly only one
line of intersection, which is called an intersecting line.
(V,W)
W
V
Two intersecting planes