three dimensional object
TRANSCRIPT
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Three-Dimensional Object
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Created By:1. Dina Ratnasari
2. Meiga Suraidha
3. Kristalina Kismadewi
4. Chairul Muhafidlin
5. Kiky Ardiana
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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
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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
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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••
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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