Geometry_semester_1.txt

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Author:
ghstechnology
ID:
82463
Filename:
Geometry_semester_1.txt
Updated:
2011-04-28 08:33:44
Tags:
geometry
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Description:
geometry
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  1. Collinear
    Points on the same line
  2. Coplaner
    points on the same plane
  3. Non collinear
    points not on the same line
  4. non coplaner
    points not on the same plane
  5. area of a Rectangle
    Base x height
  6. area of a triangle
    Base x height / 2

    b x h / 2
  7. Area of a parallelagram
    Base x Height
  8. Area of a circle
    A= Pi(r2)
  9. Circumference of a circle
    C= Pi (d)

    D= diameter
  10. diameter of a circle
    D=2r

    r=Radius
  11. Complementary angle is equal to :
    90 degrees
  12. Supplementary angle is equal to :
    180 degrees
  13. Midpoint formula
    M = (X1 + X2 / 2 , Y1+ Y2 / 2)

  14. Endpoint formula
    ( X1+ X / 2 = X2 , Y1+ Y / 2 = Y2 )
  15. Distance Formula
    D = [ ( x1-x2 )2 + ( y1-y2 )2

    [ = square root sign
  16. Linear pair
    Two angles that create a line
  17. Theorem: All verticle angles are....
    Congruent
  18. Acute angle
    Less than 90 degrees
  19. Obtuse angle
    More than 90 degrees
  20. Straight angle
    180 degrees
  21. To bisect an angle is to
    cut it in half
  22. Adjacent angles are
    next to eachother. no overlapping
  23. Conditional Statement
    A -> B
  24. Converse Statement
    B -> A
  25. Inverse Statement
    Not A -> Not B
  26. Contrapositive Statement
    Not B -> Not A
  27. Deductive Reasoning
    Uses facts to come to a conclusion
  28. Inductive Reasoning
    Uses a pattern to determine a conclusion
  29. counter Examples
    • Prove the statement is false
    • (ex. All polygons are squares. Prove wrong: Rectangles etc)
  30. Biconditional statement
    • If and only if
    • (ex. If a polygon has three sides than it is a triangle. BICONDITIONAL: A polygon has three sides if and only if {iff} it is a triangle.
  31. Perpendicular lines Form
    A right angle
  32. Law of detatchment
    if hypothesis is true, then conclusion is true
  33. Law of Syllagism
    • EX. Conclude that A -> B
    • A->N
    • N->P
    • P->B
  34. segments are congruent if and only if:
    The lengths are equal
  35. If the lines are parallel then:
    The corresponding angles are congruent
  36. If two lines are parallel than:
    The alternate interior angles are congruent
  37. If two lines are parallel than:
    the alternate exterior angles are congruent
  38. If two lines are parallel then:
    The consecutive interior angles are supplentary
  39. Slope is
    • Y = Mx + B
    • M= slope
    • B=y intercept
  40. Scalene triangle
    all different sides
  41. Isosceles triangle
    Two equal sides
  42. Equalatrial triangle
    All sides are equal
  43. Equiangular
    All angles are equal
  44. Exterior angle theorum:
    • M<1+M<2= M<3
    • (measure of angle 1 + measure of angle 2 = measure of angle three)
  45. 5 congruence thrms
    • SAS: side angle side
    • SSS: side side side
    • HL: hypotenuse and leg
    • ASA: angle side angle
    • AAS: angle angle side
  46. if two lines are parallel then their
    slopes are the same
  47. Slope formula
    Y1-Y2 / X1-X2
  48. Point slope formula
    Y-Y1=M( X-X1 )
  49. Translation
    slide
  50. reflection
    flip
  51. rotation
    turn
  52. CPCTC
    Corresponding Parts of Congruent Triangles are Congruent
  53. Midsegment of a triangle:
    Joins the midpoints. 1/2 length of the longest and parallel to longest side
  54. Concurrent:
    Where lines intersect
  55. Point of Concurrency
    The point where lines intersect
  56. Circumcenter
    Lies on a perpendicular bisector
  57. Perpendicular bisector
    perpendicular and bisects a segment
  58. incenter
    Lies on the angle bisector
  59. Median of a triangle
    Joins vertex and midpoint
  60. Centroid
    Lies on medians
  61. Altitude of a triangle
    Joins vertex and perpendicular bisector
  62. Ortocenter
    lies on the altitude
  63. Relationship between side lengths and angle measures:
    longest side opposite largest angle, shortest dise opposite smallest angle

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