Chapter 1: Tools of Geometry 1- 2 Segments, Rays, Parallel Lines and Planes

Objectives 1. To identify segments and rays. 2. To recognize parallel lines, skew lines, and parallel planes. HW/CW: pgs 25-26 #’s 2 – 24 Even

Postulates Definition: an assumption that needs no explanation. Examples: Through any two points there is exactly one line. A line contains at least two points. Through any three noncollinear points, there is exactly one plane. A plane contains at least three points.

Postulates Examples: If two planes intersect, then the intersecting is a line. If two points lie in a plane, then the line containing the two points lie in the same plane.

Segment Definition: Part of a line containing two endpoints and all points between them How to sketch: How to name:

Ray Definition: RA: is the part of a line consisting of one endpoint and all the points on one side of the endpoint How to sketch: How to name: ( the symbol RA is read as “ray RA” ) The first point represents the ray’s endpoint and the second point represents the ray’s direction.

Opposite Rays Definition: ( Opposite rays must have the same “endpoint” ) opposite rays not opposite rays

Parallel Lines Parallel lines are two lines in a plane that never meet. Arrows are used to indicate lines are parallel. The symbol used for parallel lines is ||.

Pairs of Lines In the above figure, the arrows show that line AB is parallel to line CD. With symbols we denote, || .

Skew Lines and Parallel Planes Two lines are skew if they do not intersect and are not in the same plane (not coplanar). All planes are either parallel or intersecting. Parallel planes are two planes that do not intersect.

Examples Name all segments that are parallel to Name all segments that intersect Name all segments that are skew to Name all planes that are parallel to plane ABC.

Answers Segments EF, BC, & GH. Segments DE, AB, AF & CD. Segments CH, BG, FG, & EH. Plane FGH.