G1 Point, Line, Plane Point, Line, Plane

Geometry Terms Undefined terms: words that do not have a formal definition but there is agreement about what they mean. Defined terms: Terms that can be described using known words Postulate or Axiom: Rule that is accepted without proof. Theorem: Rule that can be proved.

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

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

Collinear Points Collinear points are points that lie on the same line. (The line does not have to be visible.) A B C Collinear C A B Non collinear

Ray Definition: RA : Has one end point and in other direction carries on forever more How to sketch: How to name: ( the symbol RA is read as “ray RA” )

Opposite Rays Definition: Opposite rays are created when three points are collinear The two rays have the same “endpoint” and can be viewed as a line. opposite rays not opposite rays The end point will be between the two other points and we write X – A - Y

Segment Definition: Part of a line that consists of two points called the endpoints and all points between them. How to sketch: How to name: AB (without a symbol) means the length of the segment or the distance between points A and B.

The Segment Addition Postulate If C is between A and B, then AC + CB = AB. Example: AB = AC + CB Lesson 1-2: Segments and Rays

The Segment Addition Postulate If C is between A and B, then AC + CB = AB. Example: If AC = x , CB = 2x and AB = 12, then, find x, AC and CB. 2x x 12 Step 1: Draw a figure Step 2: Label fig. with given info. AC + CB = AB x + 2x = 12 3x = 12 x = 4 Step 3: Write an equation x = 4 AC = 4 CB = 8 Step 4: Solve and find all the answers

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

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

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

Intersection of Figures The intersection of two figures is the set of points that are common in both figures. The intersection of two different lines is a point. m Line m and line n intersect at point P. P n Continued…….

2 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.

Intersection of Two Different Planes is a Line. B P A R Plane P and Plane R intersect at the line

Lesson 1-1 Point, Line, Plane Homework p. 5 #1,5, 9,10,17 p. 12 #8,10,12, 29 Lesson 1-1 Point, Line, Plane