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## Lesson 1-1

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**Lesson 1-1**Point, Line, Plane Lesson 1-1 Point, Line, Plane**Points**• Point – a specific location in space • 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 A C Lesson 1-1 Point, Line, Plane**Lines**• Line- segment extending forever in opposite directions • Lines extend indefinitely and have no thickness or width. • How to sketch : using arrows at both ends. • How to name: several ways (1) small script letter – line n or n (2) any two points on the line - • Never name a line using three points – • 2 points make up a line n A B C Lesson 1-1 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: 3 ways (1) Capital script letter – Plane M, M, Plane ABC (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 1-1 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 1-1 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 1-1 Point, Line, Plane**Coplanar Objects**Coplanar objects (points, lines, etc.) are objects could be on the same plane. The plane does not have to be visible. Are the following points coplanar? A, B, C ? Yes Yes H, G, F, E ? E, H, C, B ? Yes A, G, F ? Yes Lesson 1-1 Point, Line, Plane**Non Coplanar**• Points that could not be connected by a plane are said to be Non Coplanar points A C B F B C E G NO NO Lesson 1-1 Point, Line, Plane**Intersection of Figures**The intersection of two figures is the list of all points that are shared by both figures. The intersection of two lines is a point. m Line m and line n intersect at point P. P n Continued……. Lesson 1-1 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 1-1 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. C B C A A B Collinear Non collinear Lesson 1-1 Point, Line, Plane**NoncollinearPoints**• Noncollinear points are points that do no lie on the same line. C A B Non collinear Lesson 1-1 Point, Line, Plane**Quadrants/ Graphs**I II ORIGIN X-Axis III IV Y-Axis Lesson 1-1 Point, Line, Plane**Postulates**Definition: An assumption that needs no explanation. Examples: Postulate #1 • Through any two points there is • exactly one line. Postulate #3 • A line contains at least two points. • Through any three points, there is • exactly one plane. Postulate #2 • A plane contains at least three non collinear points. Postulate #1 Lesson 1-2: Segments and Rays**More Postulates**Examples: • If two planes intersect, • then the intersecting is a line. • If two points lie in a plane, • then the line containing the two • points lie in the same plane. Lesson 1-2: Segments and Rays**Another Postulate**Postulate #7: If 2 lines intersect then their intersection is exactly ONE POINT What is a Theorem? A theorem is a statement that can be PROVEN true. Lesson 1-2: Segments and Rays