1 3 points, lines, planes
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This document defines key geometric concepts including points, lines, planes and their relationships. It explains that points have no size, lines extend indefinitely and planes are flat surfaces that extend without limits. It also covers topics like collinear points that lie on the same line, determining if objects are coplanar by lying on the same plane, and the different types of intersections between lines and planes, which can be a point, line or no intersection.
1 3 points, lines, planes
- 1. Lesson 1-3 Point, Line, Plane Lesson 1-3 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). Lesson 1-3 Point, Line, Plane A B A C
- 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 - Lesson 1-3 Point, Line, Plane n A B C
- 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) + 3 0 = -3 + 3 0 = 0 The point A satisfies the equation, therefore the point is collinear with the points on the line. Lesson 1-3 Point, Line, Plane A B C A B C Collinear Non collinear
- 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 Lesson 1-3 Point, Line, Plane A B C Horizontal Plane M Vertical Plane Other
- 6. Different planes in a figure: Lesson 1-3 Point, Line, Plane A B C D E F G H Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc.
- 7. Other planes in the same figure: Any three non collinear points determine a plane! Lesson 1-3 Point, Line, Plane Plane AFGD Plane ACGE Plane ACH Plane AGF Plane BDG Etc.
- 8. Coplanar Objects Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. Lesson 1-3 Point, Line, Plane 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 Yes Yes No
- 9. Intersection of Figures The intersection of two figures is the set of points that are common in both figures. Lesson 1-3 Point, Line, Plane The intersection of two lines is a point. m n P Continued……. Line m and line n intersect at point P .
- 10. 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 1-3 Point, Line, Plane
- 11. Intersection of Two Planes is a Line. Lesson 1-3 Point, Line, Plane P R A B Plane P and Plane R intersect at the line
- 12. Planes can be perpendicular.
- 13. Planes can be parallel.
- 14. Planes can be… intersecting perpendicular parallel
- 15. Homework: P. 19 (2-36 even, 37-47, 55-60 write out sentences) Lesson 1-3 Point, Line, Plane