Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Objectives What we will learn We will learn to identify and draw models of points, lines, and planes, and determine their characteristics. 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 – AB, BC, AC Never name a line using three points - n A B C Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Line Segment Line segments are straight and they have two endpoints. NO arrows on both ends! Line segments are part of a line, and come in various lengths. Below is a picture of a line segment. When we draw one, we usually use dots to emphasize the endpoints. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Line Segment How to name: using their endpoints. A or B Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Ray A ray is straight and it has one endpoint. A ray extends indefinitely (forever) in one direction. Endpoint Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Ray How to name: using its endpoint and any other point on the ray. Note: We always write the endpoint first, then the other point. CD C D 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

Lesson 1-1 Point, Line, Plane Name the planes Front: 1) 2) Back: 1) 2) Top: 1) 2) Bottom: 1) 2) Left: 1) 2) Right: 1) 2) 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

Lesson 1-1 Point, Line, Plane Postulates Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Objectives: What we’ll learn… To identify and use basic postulates about points, lines, and planes. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Definition: Postulate (Axiom): Statements in geometry that are accepted as true. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Postulate 1-1: Two points determine a unique line. m Q P There is only one line that contains point P and Q. Continued……. Lesson 1-1 Point, Line, Plane

Lesson 1-1 Point, Line, Plane Postulate 1-2: 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

Lesson 1-1 Point, Line, Plane Postulate 1-3: Three noncollinear points determine a unique plane. Ç There is only one plane that contains points A, B , and C. B A Continued……. Lesson 1-1 Point, Line, Plane

Postulate 1.4-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

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