1-1 Points, Lines, & Planes Geometry

What is a definition? Known words used to describe a new word Undefined terms – not formally defined There are 3 in geometry. Point Line Plane

Point 1. Has no __________ (no length, width, thickness) 2. Usually represented by a ________ 3. Named using one _________ letter B

Line Extends _______ in one _________ (length) Has an _____________ on each end representing the fact that it goes on forever Consists of an _______ amount of points Always ___________ Named with a _________ script letter or by ____points on the line Can be called: Line l Line AB or AB Line BA or BA l A B

Plane Extends forever in ____ dimensions (length & width) A _____ surface consisting of infinitely many points Usually represented by a _____sided figure Named with a ________ script letter or ______ points on the surface of the plane Can be named: Plane W Plane ABC, plane BCA, plane CBA, etc. A W C B

More Definitions Collinear points – points that lie on the same line Coplanar points – points that lie on the same plane

1a Name three points that are collinear. Naming Collinear and Coplanar Points 1a Name three points that are collinear. G H F E D 1b Name four points that are coplanar. 1c Name three points that are not collinear. SOLUTION • • •

Line Segment (or segment) A section of a line that has 2 endpoints Named by its endpoints. AB or BA A B

Ray Piece of a ______ with only one endpoint (initial point) and continues ________ in the other direction Named by the _________ and a _______ point named on the ray. (name MUST begin with the endpoint!) AB A B

Opposite Rays 2 rays that share a common initial point and face opposite directions. QP and QS are opposite rays. P Q S

Example 2: 2a)Draw & label points A & B. 2b)Draw & label points C & D. 2c)Draw AB. 2d)Draw BC. 2e)Draw AC. 2f)Draw DA.

Intersect – 2 or more figures intersect if they have one or more points in _______. Intersection – all points or sets of points the figures have in _________. Ex. 3)What is the intersection of: AB & DA ________ BC & AC ________ ABC & BCD ________ When 2 planes intersect, their intersection is a ______.

• Name three points that are collinear. Naming Collinear and Coplanar Points • Name three points that are collinear. G H F E D • Name four points that are coplanar. • Name three points that are not collinear. SOLUTION • Points D, E, F lie on the same line, so they are collinear. • Points D, E, F, and G lie on the same plane, so they are coplanar. Also, D, E, F, and H are coplanar. • There are many correct answers. For instance, points H, E, and G do not lie on the same line.

Assignment