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Relating lines to planes Lesson 6.1. Plane. Two dimensions (length and width) No thickness Does not end or have edges Labeled with lower case letter in one corner. m. A. B. m. C. Coplanar. Points, lines or segments that lie on a plane. B. A. C. m. Non-Coplanar
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Plane • Two dimensions (length and width) • No thickness • Does not end or have edges • Labeled with lower case letter in one corner m
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
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.
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
2. Theorem 45: A line and a point not on the line determine a plane.
3. Theorem 46: Two intersecting lines determine a plane.
4. Theorem 47: 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 m Y
m P2: If two planes intersect, their intersection is exactly one line. n
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
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