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Lesson 1-2 Point, Line, Plane 1 Lesson 1-2 Point, Line, Plane.

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Presentation on theme: "Lesson 1-2 Point, Line, Plane 1 Lesson 1-2 Point, Line, Plane."— Presentation transcript:

1 Lesson 1-2 Point, Line, Plane 1 Lesson 1-2 Point, Line, Plane

2 Lesson 1-2 Point, Line, Plane 2 Points Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the same letter (in the same sketch). A B AC

3 Lesson 1-2 Point, Line, Plane 3 Lines Lines extend indefinitely and have no thickness or width. How to sketch : using arrows at both ends. How to name: 2 ways (1) small script letter – line n (2) any two points on the line - Never name a line using three points - n A B C

4 Lesson 1-2 Point, Line, Plane 4 Collinear Points Collinear points are points that lie on the same line. (The line does not have to be visible.) A point lies on the line if the coordinates of the point satisfy the equation of the line. Ex: To find if A (1, 0) is collinear with the points on the line y = -3x + 3. Substitute x = 1 and y = 0 in the equation. 0 = -3 (1) = = 0 The point A satisfies the equation, therefore the point is collinear with the points on the line. ABC A B C Collinear Non collinear

5 Lesson 1-2 Point, Line, Plane 5 Planes A plane is a flat surface that extends indefinitely in all directions. How to sketch: Use a parallelogram (four sided figure) How to name: 2 ways (1) Capital script letter – Plane M (2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA A B C Horizontal Plane M Vertical PlaneOther

6 Lesson 1-2 Point, Line, Plane 6 Different planes in a figure: A B CD E F G H Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc.

7 Lesson 1-2 Point, Line, Plane 7 Other planes in the same figure: Any three non collinear points determine a plane! Plane AFGD Plane ACGE Plane ACH Plane AGF Plane BDG Etc.

8 Lesson 1-2 Point, Line, Plane 8 Coplanar Objects Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. Are the following points coplanar? A, B, C ? A, B, C, F ? H, G, F, E ? E, H, C, B ? A, G, F ? C, B, F, H ? Yes No Yes No

9 Lesson 1-2 Point, Line, Plane 9 Postulates or Axioms Definition: An assumption that needs no explanation. Accepted statement of fact Examples: Postulate 1-1: Through any two points there is exactly one line.

10 Lesson 1-2 Point, Line, Plane 10 Intersection of Figures The intersection of two figures is the set of points that are common in both figures. Postulate 1-2: The intersection of two lines is a point. m n P Continued……. Line m and line n intersect at point P.

11 Lesson 1-2 Point, Line, Plane 11 Postulate 1-3: Intersection of Two Planes is a Line. P R A B Plane P and Plane R intersect at the line

12 Lesson 1-2 Point, Line, Plane 12 3 Possibilities of Intersection of a Line and a Plane (1) Line passes through plane – intersection is a point. (2) Line lies on the plane - intersection is a line. (3) Line is parallel to the plane - no common points.


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