Lesson 1-1 Point, Line, Plane 1 Geometry Lesson 1-1 Point, Line, Plane 2 Points do not have actual size. How to Sketch: Using dots A B C A How to label: Use capital letters Never name two points with the same letter (in the same sketch). Lesson 1-1 Point, Line, Plane 3 • A is a measure of length, width, or height. length Lesson 1-1 Point, Line, Plane 4 Lines extend indefinitely and have no thickness or width. A line is 1 dimensional (length) How to sketch : using arrows at both ends. n A B How to name: 2 ways C (1) small script letter – line n AB , BC, AC , BA, CA, CB (2) any two points on the line Never name a line using three points – Symbol ABC Lesson 1-1 Point, Line, Plane 5 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 A B the points on the line y = -3x + 3. Substitute x = 1 and y = 0 in the equation. Collinear 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 1-1 Point, Line, Plane C 6 Points that do NOT lie on the same line Points A, B, & A B D C C are… Non collinear C A E Lesson 1-1 Point, Line, Plane B Non collinear 7 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 M C Horizontal Plane Vertical Plane Lesson 1-1 Point, Line, Plane Other 8 A D B C E H Plane ABCD Plane EFGH F G Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc. Lesson 1-1 Point, Line, Plane 9 Any three non collinear points determine a plane! A D B Plane AFGD Plane ACGE C Plane ACH E H F G Plane AGF Plane BDG Etc. Lesson 1-1 Point, Line, Plane 10 Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. A D B C E H F G 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 ? Lesson 1-1 Point, Line, Plane Yes No Yes Yes Yes No 11 The intersection of two figures is the set of points that are common in both figures. The intersection of two lines is a point. m Line m and line n intersect at point P. P n Lesson 1-1 Point, Line, Plane Continued……. 12 (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 13 B AB P A R Plane P and Plane R intersect at the line Lesson 1-1 Point, Line, Plane 14 • Is straight and made up of points • Has a definite beginning and definite end Name a line segment by using the endpoints only You will always use two letters to name a segment Symbol • • • Name of these segments: Name of segment from -2 to 0. Lesson 1-1 Point, Line, Plane 15 Is straight and made up of points Has a beginning but no end Starting pt. of a ray is called the endpoint Name a ray by using the endpt. 1st and another point on the ray You will always use two letters to name a ray Symbol Names of these rays: Lesson 1-1 Point, Line, Plane 16