Math Chapter 2

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deamon
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38805
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Math Chapter 2
Updated:
2010-09-30 19:48:14
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Tx Chapter
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to help study for math in texas geometry 2
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  1. Define: Conjecture
    an unproven statement that is based on observations
  2. Define: Inductive reasoning
    when you find a pattern in specific cases and then wright a conjecture for the general cause
  3. Define: Counterexample
    a specific case for which the conjecture is false
  4. what is the counterexample in...

    2x>x
    • 2(-1)>-1
    • -2>-1 False
  5. Define: conditional statement
    • a logical statement that has 2 parts, a hypothesis and a conclusion. It is written in a
    • if-then form
  6. Define: biconditional statements
    a statement that contains the phrase "if and only if"

    • Example: an angle is a right angle if and only if its angle measurement is equal to
    • 90 degrees
  7. Define: law of syllogism
    • if hypothesis A, then conclusion B
    • if hypothesis B, then conclusion C
    • if hypothesis A, then conclusion C
  8. Define: law of detachment
    Law of Detachment ( also known as Modus Ponens (MP) ) says that if p=>q is true and p is true, then q must be true.

    • example:If an angle is obtuse, then it cannot be acute.
    • Angle A is obtuse.
    • ThereforeAngle A cannot be acute.
  9. Postulate 1: ruler postulate
    The points of a line can be matched one to one with the real numbers. The real numbers that correspond to a point is the coordinate
  10. Postulate 2: segment addition postulate
    • If B is between A and C, then AB+BC=AC
    • If AB+BC=AC, then B is between A and C
  11. Postulate 4: angle addition postulate
    If P is in the interion of <RST, then the measure of <T=RST is equal to the sum of the measure of <RSP and <PST
  12. Postulate 5
    Through any two points there exists exactly one line
  13. Postulate 6
    A line contains at least two points
  14. Postulate 7
    If two lines intersect, then their intersection is exactly one point
  15. Postulate 8
    through any three noncolinear points there exists exactly one plane
  16. Postulate 9
    A plane contains at least three noncolinear points
  17. Postulate 10
    If two points lie in a plane, then the line containing them lies in the plane
  18. Postulate 11
    If two planes intersect, then their intersection is a line
  19. Define: line perpendicular to a plane
    a line perpendicular to a plane if and only if the three line intersects in a point ane is perpendicular to every line in that planethat intersects it at that point
  20. Addition Property
    If a=b, then a+c=b+c
  21. subtraction property
    If a=b, then a-c=b-c
  22. multiplication property
    If a=b, then ac=ab
  23. division property
    If a=b and c is not equal to 0, then a/c=b/c
  24. Subsitution property
    If A=b, then "A" can be subsituted for b in any equation or expression
  25. Distributive property
    a(b+c)=ab+ac, where a, b, and c, are real numbers
  26. Reflexive property
    A=A
  27. Symmetric property
    If a=b, then b=a
  28. Transative property
    If a=b and b=c, then a=c
  29. Theorm 2.3: Right angles congruence theorem
    All right angle are congruent
  30. Theorem 2.4: congruent supplements theorem
    If two angles are supplementry to the same angle, then they are congruent
  31. Theorem 2.5: congruent complements theorem
    If two angles are complementry to the same angle , then they are congruent
  32. Postulate 12: linear pair postulate
    If two angles form a linear pair, then they are supplementary
  33. Theorem 2.6: vertical angles congruence theorem
    Vertical angles are congruent

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