1. Relating lines to planes Lesson 6.1 Dedicated To Graham Millerwise

2. 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

3. 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

4. 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

5. 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 points - many planes n 1.

6. Theorem 45: A line and a point not on the line determine a plane. 2.

7. Theorem 46: Two intersecting lines determine a plane. 3.

8. 4.Theorem 47: Two parallel lines determine a plane.

9. Two postulates concerning lines and planes Postulate 1: If a line intersects a plane not containing it, then the intersection is exactly one point. X C Y m

10. Postulate 2: If two planes intersect, their intersection is exactly one line. m n

11. 1.m Ո n = ___ 2.A, B, and V determine plane ___ 3.Name the foot of RS in m. 4.AB and RS determine plane ____. 5.AB and point ______ determine plane n. 6.Does W line in plane n? 7.Line AB and line ____ determine plane m. 8.A, B, V, and _______ are coplanar points. 9.A, B, V, and ______ are noncoplanar points. AB m P R or S n No VW W or P

12. A P B C m Given: ABC lie in plane m PB  AB PB  BC AB  BC Prove: <APB  <CPB 1.PB  AB, PB  BC 2.  PBA &  PBC are rt  s 3.  PBA   PBC 4.AB  BC 5.PB  PB 6.ΔPBA  ΔPBC 7.  APB   CPB 1.Given 2.  lines form rt  s 3.Rt  s are  4.Given 5.Reflexive Property 6.SAS (4, 3, 5) 7.CPCTC