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2013-01-14 19:44:29
Math Notes final

Final geometry math notes
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  1. Collinear Points
    2 points that make up a line
  2. Plane
    Flat surface with no thickness
  3. Line segment
    Segment of a line with an end point
  4. Opposite rays
    Form a line while sharing a point
  5. Skew lines
    Non-coplanar, never intersecting lines
  6. Congruent segments
    2 segments with the same length
  7. Perpendicular bisector
    Line, segment or ray that is perpendicular to the segment at the midpoint
  8. Angle bisector
    A ray that divides an angle into two congruent coplanar angles
  9. Complementary angles
    Add to 900
  10. Supplementary angles
    Add to 1800
  11. Adjacent angles
    2 angles next to each other that share a side
  12. Vertical angles
    • formed by 2 lines intersecting
    • They are congruent
  13. point slope form
  14. Conjectures
    Logical conclusions based on reasoning
  15. Counterexamples
    One example to show a conjecture is false
  16. Conditional statements
    • if-then statements
    • p-> q
  17. Hypothesis
    • The part that follows the if
    • p
  18. Conclusion
    • Part that follows the "then"
    • q
  19. Converse
    • Reverse of the conditional
    • q->p
  20. Biconditional
    • conditional and converse are true
    • p<->q
  21. Deductive reasoning
    Process of reasoning logically from given statements to reach a conclusion
  22. Detachment
    • If the conditional is T; + hypothesis is T then conclusion is T
    • p->q is T, p-> T, then q->T
  23. Syllogism
    2 conditionals if conclusion of one being the hypothesis of next
  24. Addtional equality property
    if a=b then a+c=b+c
  25. Equality property of Subtraction
    if a=b then a-c=b-c
  26. Equality property of Multiplication
    if a=b then ac=bc
  27. Equality property of divsion
    if a=b then a/c=b/c
  28. Reflexive equality property
  29. Symmetric property of equality
    if a=b then b=a
  30. Transitive property of equality
    a=b then b can replace a anywhere
  31. Distributive property of equality
    if a(b+c) =ab+ac
  32. SSI Same side interior angles (between parallels)
    Are congruent angles
  33. Transversal line
    Crosses both lines
  34. AIA alternate interior angles
    Are congruent
  35. Therom 3-10
    if 2 lines are perpendicular to the same line then they are parallel to each other
  36. Equilateral triangle
    Three sides are equal
  37. Isosceles
    Two sides are equal length
  38. Scalene
    All sides are different length
  39. Polygon
    A closed plane
  40. Total degrees in a polygon
  41. Slope intercept form
  42. standard form
  43. point slope form
  44. SAS side-angle-side
    Same side, angle and another side
  45. SSS Side side side
    three side are all congruent
  46. AAA
    Doesn't work
  47. ASA
    Equal angle, side and another angle
  48. SAA/AAS
    Side Angle Angle
  49. H-L therom
    • 1. 2 right angles
    • 2. Triangles have congruent hypotenuses
    • 3. A pair of congruent legs
    • SSA works here
  50. Hypotenuse
    Side opposite of the right anle/vertex
  51. CPCTC
    Corresponding pars of congruent triangles are congruent
  52. Triangle midsegment theorem
    midsegment parallel = 2(midsegment)
  53. Theorem 5-2
    If a point is the perp. bisector of a segment then it is equidistant from the endpoints of the segment
  54. Theorem 5-3
    If a point is equidistant from both endpoints then it must be on the perp. bisector
  55. Locus
    Set of all points that meet a condition
  56. Theorem 5-4
    If a point is on the bisector of an angle then it is equidistant to each side of angles
  57. Theorem 5-5
    Th. 5-4 converse