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6.1 Lines and Planes

6.1 Lines and Planes. Objectives: Understand the basic concepts relating to planes Know the 4 ways to determine a plane. Apply two postulates concerning lines and planes. A. B. C.

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6.1 Lines and Planes

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  1. 6.1 Lines and Planes • Objectives: • Understand the basic concepts relating to planes • Know the 4 ways to determine a plane. • Apply two postulates concerning lines and planes

  2. A B C Plane: a surface such that if any two points are connected by a line, all points of the line are also on the surface. m plane m or plane ABC (noncollinear points)

  3. A B C How many points determine a line? How do we determine a plane? m 1. Three noncollinear points determine a plane.

  4. B m 2. A line and a point not on the line determine a plane.

  5. m 3. Two intersecting lines determine a plane.

  6. m 4. Two parallel lines determine a plane.

  7. E F Postulate: If a line intersects a plane not containing it, then the intersection is exactly one point. (called the foot) m

  8. S R Postulate: If 2 planes intersect, then their intersection is exactly one line. n m

  9. Postulate: If 2 planes intersect, then their intersection is exactly one line. n m S R

  10. n R W A B V m S Example 1: Answer the questions: P

  11. n Example 1: Answer the questions: R A B V m S

  12. n R W A B V m S Example 1: Answer the questions: m∩ n = ____. Is W in plane n? A, B, & V determine plane _____. Name the foot of RS in m. AB & RS determine plane _____. A, B, V & ____ are coplanar points. A, B, V & ____ are noncoplanarpoints. AB and point ____ determine plane m. Line AB & Line ____ determine plane m. R & S lie in plane n, what about RS? P

  13. P C B A m Definition of perpendicular ABP and CBP are right angles ABP  CBP All right angles are congruent Given Reflexive Property ∆ABP  ∆CBP SAS APB  CPB CPCTC

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