Three-Dimensional Object

Created By:1. Dina Ratnasari

2. Meiga Suraidha

3. Kristalina Kismadewi

4. Chairul Muhafidlin

5. Kiky Ardiana

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

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

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••

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

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

Ag

h

Two parallel lines on the same plane

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

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

vPoint A is outside plane V

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

hPg

V Line G intersect line h

V

hg

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

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

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

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

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