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## Lesson 1-2

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**Lesson 1-2**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**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 A C 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**Line Segment**• Line segments are straightand they have twoendpoints. • 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**Line Segment**• How to name: using their endpoints. A or B 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**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**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**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:**A 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**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**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 1-3**Postulates 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**Definition:**Postulate (Axiom): Statements in geometry that are accepted as true. 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**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**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