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# 1 3 points, lines, planes

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### 1 3 points, lines, planes

1. 1. Lesson 1-3 Point, Line, Plane Lesson 1-3 Point, Line, Plane
2. 2. Points <ul><li>Points do not have actual size. </li></ul><ul><li>How to Sketch: </li></ul><ul><li> Using dots </li></ul><ul><li>How to label: </li></ul><ul><li>Use capital letters </li></ul><ul><li>Never name two points with the same letter </li></ul><ul><li>(in the same sketch). </li></ul>Lesson 1-3 Point, Line, Plane A B A C
3. 3. Lines <ul><li>Lines extend indefinitely and have no thickness or width. </li></ul><ul><li>How to sketch : using arrows at both ends. </li></ul><ul><li>How to name: 2 ways </li></ul><ul><li>(1) small script letter – line n </li></ul><ul><li>(2) any two points on the line - </li></ul><ul><li>Never name a line using three points - </li></ul>Lesson 1-3 Point, Line, Plane n A B C
4. 4. Collinear Points <ul><li>Collinear points are points that lie on the same line. (The line does not have to be visible.) </li></ul><ul><li>A point lies on the line if the coordinates of the point satisfy the equation of the line. </li></ul><ul><li>Ex: To find if A (1, 0) is collinear with </li></ul><ul><li>the points on the line y = -3x + 3. </li></ul><ul><li>Substitute x = 1 and y = 0 in the equation. </li></ul><ul><li>0 = -3 (1) + 3 </li></ul><ul><li>0 = -3 + 3 </li></ul><ul><li>0 = 0 </li></ul><ul><li>The point A satisfies the equation, therefore the point is collinear </li></ul><ul><li>with the points on the line. </li></ul>Lesson 1-3 Point, Line, Plane A B C A B C Collinear Non collinear
5. 5. Planes <ul><li>A plane is a flat surface that extends indefinitely in all directions. </li></ul><ul><li>How to sketch: Use a parallelogram (four sided figure) </li></ul><ul><li>How to name: 2 ways </li></ul><ul><li>(1) Capital script letter – Plane M </li></ul><ul><li>(2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA </li></ul>Lesson 1-3 Point, Line, Plane A B C Horizontal Plane M Vertical Plane Other
6. 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. 7. Other planes in the same figure: <ul><li>Any three non collinear points determine a plane! </li></ul>Lesson 1-3 Point, Line, Plane Plane AFGD Plane ACGE Plane ACH Plane AGF Plane BDG Etc.
8. 8. Coplanar Objects <ul><li>Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. </li></ul>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. 9. Intersection of Figures <ul><li>The intersection of two figures is the set of points that are common in both figures. </li></ul>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. 10. 3 Possibilities of Intersection of a Line and a Plane <ul><li>(1) Line passes through plane – intersection is a point. </li></ul><ul><li>(2) Line lies on the plane - intersection is a line. </li></ul><ul><li>(3) Line is parallel to the plane - no common points. </li></ul>Lesson 1-3 Point, Line, Plane
11. 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. 12. Planes can be perpendicular.
13. 13. Planes can be parallel.
14. 14. Planes can be… intersecting perpendicular parallel
15. 15. Homework: <ul><li>P. 19 (2-36 even, 37-47, 55-60 write out sentences) </li></ul>Lesson 1-3 Point, Line, Plane