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Three dimensional object

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  • 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