Lesson 1-1 Point, Line, Plane 1

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 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 1-1 Point, Line, Plane 3 A B AC

A is a measure of length, width, or height. Lesson 1-1 Point, Line, Plane 4 length

 Lines extend indefinitely and have no thickness or width.  A line is 1 dimensional (length)  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 –  Symbol Lesson 1-1 Point, Line, Plane 5 n A B C

 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) = = 0 The point A satisfies the equation, therefore the point is collinear with the points on the line. Lesson 1-1 Point, Line, Plane 6 ABC Collinear

Lesson 1-1 Point, Line, Plane 7 A C B Non collinear Points that do NOT lie on the same line  Points A, B, & C are… Non collinear A B C D E

 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 1-1 Point, Line, Plane 8 A B C Horizontal Plane M Vertical PlaneOther

Lesson 1-1 Point, Line, Plane 9 A B CD E F G H Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc.

Any three non collinear points determine a plane! Lesson 1-1 Point, Line, Plane 10 Plane AFGD Plane ACGE Plane ACH Plane AGF Plane BDG Etc.

Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. Lesson 1-1 Point, Line, Plane 11 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 No

The intersection of two figures is the set of points that are common in both figures. Lesson 1-1 Point, Line, Plane 12 The intersection of two lines is a point. m n P Continued……. Line m and line n intersect at point P.

(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

Lesson 1-1 Point, Line, Plane 14 P R A B Plane P and Plane R intersect at the line

Lesson 1-1 Point, Line, Plane 15 Name of these segments: A B C D E F G H Name of segment from -2 to 0. 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

Lesson 1-1 Point, Line, Plane 16 Names of these rays:  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