Warm Up

6.1 Relating lines to planes Obj: understand basic concepts to planes Identify four methods of determining a plane Apply two postulates concerning lines and planes Obj: understand basic concepts to planes Identify four methods of determining a plane Apply two postulates concerning lines and planes

Plane  Two dimensions (length and width)  No thickness  Does not end or have edges  Labeled with lower case letter in one corner  Two dimensions (length and width)  No thickness  Does not end or have edges  Labeled with lower case letter in one corner m

Coplanar Points, lines or segments that lie on a plane Non-Coplanar Points, lines or segments that do not lie in the same plane A B C m A C B m

Definition: Point of intersection of a line and a plane is called the foot of the line. B is the foot of AC in the plane m. A C B m

4 ways to determine a plane Three non-collinear points determine a plane One point - many planes Two points - one line or many planes Three linear point - many planes 1. n n

T45: A line and a point not on the line determine a plane. 2.

T46: Two intersecting lines determine a plane. 3.

4. T47: Two parallel lines determine a plane.

Two postulates concerning lines and planes P1: If a line intersects a plane not containing it, then the intersection is exactly one point. X C Y m

P2: If two planes intersect, their intersection is exactly one line. m n

A P B C m Given: ABC lie in plane m PB  AB PB  BC AB  BC Prove: <APB  <CPB