Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane 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). A B C A Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane 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 - n A B C Lesson 1-1 Point, Line, Plane

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. 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. A B C Collinear C A B Non collinear Lesson 1-1 Point, Line, Plane

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: 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 M B C Horizontal Plane Vertical Plane Other Lesson 1-1 Point, Line, Plane

Different planes in a figure: 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

Lesson 1-1 Point, Line, Plane Coplanar Objects Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible. Are the following points coplanar? A, B, C ? Yes A, B, C, F ? No H, G, F, E ? Yes E, H, C, B ? Yes A, G, F ? Yes C, B, F, H ? No Lesson 1-1 Point, Line, Plane

Intersection of Figures 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 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

Intersection of Two Planes is a Line. B P A R Plane P and Plane R intersect at the line Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Postulate or Axiom A postulate or axiom is an accepted statement as fact. Postulate and Axioms have no formal proof they exist or are true Many mathematicians do years of research trying to prove postulates or axioms true. Postulates and axioms that are proven true are known as Theorems. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Postulate 1-1 Through any two points there is exactly one line. Line t is the only line that passes through points A and B. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Postulate 1-2 If two lines intersect they intersect in exactly one point and intersect at C. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Postulate 1-3 If two planes intersect, then they intersect in exactly one line. Plane RST and Plane STW Intersect in . Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Postulate 1-4 Through any three noncollinear points there is exactly one plane. “Think of a tripod” Lesson 1-1 Point, Line, Plane