Relating lines to planes Lesson 6.1

1. Relating lines to planesLesson 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 m

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

4. A B m C 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.

5. 4 ways to determine a plane 1. Three non-collinear points determine a plane. One point - many planes Two points - one line or many planes Three linear points - many planes n

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

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

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 m Y

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

11. mՈn = ___ • A, B, and V determine plane ___ • Name the foot of RS in m. • AB and RS determine plane ____. • AB and point ______ determine plane n. • Does W line in plane n? • Line AB and line ____ determine plane m. • A, B, V, and _______ are coplanar points. • A, B, V, and ______ are noncoplanar points. AB m P n R or S No VW W or P R or S

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