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2010-10-29 00:05:49
theorems postulates

theorems and postulates
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  1. Postulate 2-1
    Through any 2 points there is exactly 1 line
  2. Postulate 2-2
    Through any 3 collinear points there its exactly 1 plane
  3. Postulate 2-3
    A line contains at least 2 points
  4. Postulate 2-4
    A plane contains at least 3 points, not all on the same line
  5. Postulate 2-5
    If 2 points lie on a plane, then the entire line containing those 2 points lies in that plane
  6. Postulate 2-6
    2 lines intersect in exactly one point
  7. Postulate 2-7
    2 planes intersect in a line
  8. Midpoint Theorem
    If M is mp of (segment) AB then (segment) AM is congruent to (segment) MB
  9. Ruler Postulate
    The points on any line or line segment can be paired with real numbers so that given any 2 points, A and B on a line, A corresponds to zero, and B corresponds to a positive real number
  10. Segment Addition Postulate
    • If A, B and C are collinear and B is between A and C, then AB + BC= AC.
    • If AB+BC=AC then B is between A and C.
  11. Theorem 2.2
    Congruence of segments is reflexive, symmetric & transitive
  12. Protractor Postulate
    Given (ray) AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of (ray) AB, such that the measure of the angle formed is r.
  13. Angle Addition Postulate
    If R is in the interior of <PQS then the m<PQR and the m<RQS= the m<PQS
  14. Supplement Theorem
    If 2 <'s form a linear pair, then they are supplemenetary
  15. Complement Theorem
    If the noncommon sides of 2 adjacent angles form a right angle, then the angles are complementary angles.
  16. Theorem 2.6
    Angles supplementary to the same angle or to congruent angles are congruent
  17. Theorem 2.7
    Angles complementary to the same angle or to congruent angles are congruent
  18. Theorem 2.9
    Perpendicular lines intersect to form 4 right anlges
  19. Theorem 2.10
    ALL right angles are congruent
  20. Theorem 2.11
    Perpendicular lines form congruent adjacent angles.
  21. Theorem 2.12
    If 2 <'s are congruent and supplementary, then each angle is a right angle
  22. Theorem 2.13
    If 2 congruent <'s form a linear pair, then they are right angles.
  23. Vertical Angles's Theorem (2.8)
    Vertical Angles are Congruent

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