geometry FINALS

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Author:
brendabelle
ID:
55351
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geometry FINALS
Updated:
2010-12-12 17:14:30
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geometry
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finals
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  1. a rule that is accepted without proof
    postulate/axiom
  2. the real number that corresponds to a point
    coordinate
  3. the absolute value of the difference of the coordinates of A & B
    distance
  4. two angles that share a common vertex & side but have no common interior points
    adjacent angles
  5. two adjacent angles whose noncommon sides are opposite rays.
    linear pair
  6. two angles whose sides form two pairs of opposite rays
    vertical angles
  7. a closed plane figure
    polygon
  8. in a polygon if no line that contains a side of the polygon contains a point in the interior of the polygon
    convex
  9. a polygon that is not conves
    concave
  10. the distance around a fugure
    perimeter
  11. the distance around a circle
    circumference
  12. the amount of surface covered by a figure
    area
  13. an unproven statement based on observations
    conjecture
  14. find a pattern in specific cases & then write a conjecture for the general case
    inductive reasoning
  15. a specific case for which the conjecture is false
    counterexample
  16. a logical statement that has 2 parts a hypothesis & a conclusion
    conditional statement
  17. a statement that is the opposite of the original statement
    negation
  18. uses facts definitions accepted properties & laws of logic
    deductive reasoning
  19. a = b, then a + c = b + c
    addition prop
  20. a = b then a - c = b - c
  21. subtraction prop
  22. a=b & c does not = 0 then a/c = b/c
    division prop
  23. a = b ac=bc
    multiplication prop
  24. a logical arguement that shows a statement is true.
    proof
  25. has numbered statements & corresponding reasons
    two-column proof
  26. a statement that can be proven
    theorem
  27. all right angles are congruent
    right angles congruence theorem
  28. if two angles are supplementary to the same angle (or to congruent angles) then they are congurent
    • congruent supplements theorem
    • same for complements
  29. if two angles form a linear pair then they are supplementary
    LINEAR PAIR POSTULATE
  30. vertical angles are congruent
    vertical angles congruence theorem
  31. two lines that do not intersect & are coplanar
    parllel lines
  32. two lines that do not intersect & are not coplanar
    skew lines
  33. is there if a line and a point not on the line, then there if exactly one line through the point parallel to the given line
    parallel postulate
  34. if there is a line & a point not on the line, then there is exactly one line through the point perpendicular to the given line
    perpendicular postulate
  35. a line that intersects two or more coplanar lines & different points
    transversal
  36. if two lines are parallel to the same line, then they are parallel to each other
    transitive property of parallel lines
  37. in a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope
    slopes of parallel lines
  38. two nonvertical lines are perpendicular if & only if the product of their slopes id -1
    slopes of perpendicular lines
  39. if a transversal is perpendicular to 1 of 2 parallel lines, then it is perpendicular to the other
    perpendicular transversal theorem
  40. in a plane if two lines are perpendicular to the same line, then they are parallel to each other
    lines perpendicular to a transversal theorem
  41. the original angles
    interior angles
  42. the angles that form linear pairs w/ the interior angles are the
    exterior angles
  43. the sum of the measures of the interior angles of a triangle is 180
    triangle sum theorem
  44. the measure of an exterior angle of a triangle is = tot he sum of the measures of the two nonadjacent interior angles
    exterior angle theorem
  45. a statement that can be proved easily using the theorem
    corollary to a theorem
  46. the acute angles of a right angle are complementary
    corollary to the triangle sum theorem
  47. if two angles of one triangle are congruent to two angles of another triangle, then the 3rd angles are also congruent
    third angles theorem
  48. if two sides of a triangle are congruent then the angles opposite them are congruent
    base angles theorem
  49. if two angles of a triangle are congruent then the angles opposite them are congruent
    converse of base angles theorem
  50. if a triangle if equilateral then it is equiangular
    corollary to the base angles theorem
  51. if a triangle is equiangular, then it is equilateral
    corollary to the converse of base angles theorem
  52. an operation that moves or changes a geometric figure in some way to produce a new figure
    transformation
  53. the new figure
    image
  54. moves every point of a figure the same direction & distance
    translation
  55. uses a line of reflection to create a mirror image of the original figure
    reflection
  56. turns a fig. around a fixed point
    rotation
  57. a segment that connects the midpoints of two sides of the triangle
    midpoint of the triangle
  58. the segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side & is half as long as that side
    midsegment theorem
  59. a seg., ray, line, or plane that is perpendicular to a segment @ its midpoint
    perpendicular bisector
  60. same distance form each point
    equidistant
  61. in a plane if a point is on the perpendicular bisector of a seg. then it is equidistant from the endpoints of the seg.
    perpendicular bisector theorm
  62. in a plane if a point is equidistant from the endpoints of a seg. then it is on the perpendicular bisector of the segment
    converse of the perpendicular bisector theorem
  63. when three or more lines,rays, or segs. intersect in the same point
    • concurrent
    • the point is the point of concurrency
  64. the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle
    concurrency of perpendicular bisectors of a triangle
  65. the point of concurrency of the 3 perpendicular bisectors
    circumcenter
  66. if a point is on the bisector of an angle, then it is equidistant form the two sides of the angle
    angle bisector theorem
  67. if a point is in the interior of an angle & is equidistant from the sides of the angle then it lies on the bisector of the angle
    converse of the angle bisector theorem
  68. the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle
    concurrency of angle bisectors of a triangle
  69. the point of concurrency of the 3 angle bisectors of a triangle
    incenter
  70. a segment from a vertex to the midpoint of the opposite side.
    median of triangle
  71. point of concurrency of the medians of a triangle
    centroid
  72. the medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.
    concurrency of medians of a triangle
  73. the perpendicular segment from vertex to the opposite side or line that contains the opposite side
    altitude of a triangle
  74. the lines containing the altitudes of a triangle are concurrent
    concurrency of altitudes of a triangle
  75. the point of concurrency for ltitudes
    orthocenter
  76. the sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side
    triangle inequality theorem
  77. if two sides of one triangle are congruent to two sides of another triangle & the includes angle of the 1st is larger than the included angle of the 2nd then the third side of the 1st is longer then the 3rd of the second
    hinge theorem
  78. if two sides of one triangle are congruent to two sides of another triangle & the third side of the first is longer than the third side of the second then the included angle of the first is larger than the included angle of the second
    converse of the hinge theorem

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