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## Lesson 1-2

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**Lesson 1-2**Point, Line, Plane Lesson 2 Point, Line, Plane**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 C Lesson 2 Point, Line, Plane**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 Lesson 2 Point, Line, Plane**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) + 3 0 = -3 + 3 0 = 0 The point A satisfies the equation, therefore the point is collinear with the points on the line. A B C Collinear C A B Non collinear Lesson 2 Point, Line, Plane**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 M B C Horizontal Plane Vertical Plane Other Lesson 2 Point, Line, Plane**Different planes in a figure:**A B Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc. D C E F H G Lesson 2 Point, Line, Plane**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. Lesson 2 Point, Line, Plane**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 ? Yes A, B, C, F ? No H, G, F, E ? Yes E, H, C, B ? Yes A, G, F ? Yes C, B, F, H ? No Lesson 2 Point, Line, Plane**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. Lesson 2 Point, Line, Plane**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 Line m and line n intersect at point P. P n Continued……. Lesson 2 Point, Line, Plane**Postulate 1-3: Intersection of Two Planes is a Line.**R B P A Plane P and Plane R intersect at the line Lesson 2 Point, Line, Plane**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. Lesson 2 Point, Line, Plane