BJU 1.1-1.5 Geometry

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Author:
alyzapinski13
ID:
33610
Filename:
BJU 1.1-1.5 Geometry
Updated:
2010-09-09 02:23:57
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BJU Geometry
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Description:
Geometry, including postulates, theorems, & terms from BJUpressonline
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  1. SETS
    • A collection of elements
    • -List method: P={red, blue, yellow}
    • -Set Builder Notation: P={x l x is a primary color}
  2. ELEMENT
    E symbol= "is an element of"

    -V={8,9,10}

    9 E V
  3. EQUIVELENT SETS
    sets that have the same # of elements
  4. EQUAL SETS
    sets that are identicle
  5. SUBSET
    C = if set A contains set B.... B c A

    • A={1,2,3,4,5}
    • B={1,2,3}
  6. PROPER SUBSET
    • a proper subset is a subset that is not the set itself.
    • OR, two sets cannot be equal.
  7. BINARY AND UNARY
    • Has to do with 2 sets....
    • Has to do with 1 set.
  8. UNION
    U= The combo of two sets
  9. INTERSECTION
    n= The common elements of two sets
  10. DISJOINT SETS
    • two sets with nothing in common
    • (empty set symbol of slashed circle)
  11. COMPLEMENT
    all of the elements NOT given in a set

    • u={xlx E colors}
    • P={xlx E primary}
    • SO.... P'={xlx "slashed element sign" primary}
  12. Collinear Points
    points that lie on the same line
  13. NONCOLLINEAR POINTS
    points that do not lie on the same line
  14. CONCURRENT LINES
    lines that intersect at a single point
  15. COPLANAR POINTS
    points that lie on the same plane
  16. COPLANAR LINES
    Lines that lie on the same plane
  17. PARRALLEL LINES
    coplanar lines that do NOT intersect
  18. SKEW LINES
    lines that are NOT coplanar
  19. PARALLEL PLANES
    planes that do NOT intersect
  20. POSTULATE
    basic statements from which the theorems are proved
  21. THEOREM
    a statement that can be logically proved using a DEFINITION, POSTULATE, or PREVIOUSLY PROVED THEOREM.
  22. EXPANSION POSTULATE
    • a line contains at least 2 points;
    • a plane contains at least 3 noncollinear points;
    • space contains at least 4 noncoplanar points.
  23. LINE POSTULATE
    any 2 points in space lie in exactly 1 line
  24. PLANE POSTULATE
    3 noncollinear points lie in exactly one plane
  25. FLAT PLANE POSTULATE
    • if 2 points lie in a plane,
    • then the line containing these 2 points lie in the same plane
  26. PLANE INTERSECTION POSTULATE
    if 2 planes intersect, than their intersection is exactly 1 line
  27. THEOREM 1.1
    • if any 2 distinct lines intersect,
    • they intersect at one & only one point.
  28. THEOREM 1.2
    a line & a point not on that line are contained in one & only one plane
  29. THEOREM 1.3
    2 intersecting lines are contained in one & only one plane
  30. THEOREM 1.4
    2 parallel lines are contained in one & only one plane

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