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Geometry Regents Reveiw

  1. Conjunction (And Statements)
    Squares are parallelograms and trapezoids are circles

    BOTH PARTS must be true to be true

    T and F therefore the statement is false!
  3. Equation of a circle (MEMORIZE THISS!)
    Image Upload 2

    • where (h, k) is the center
    • r = radius
  4. Disjunction (or Statements)

    Squares are parallelograms OR trapezoids are circles.
    One piece needs to be true for this to be true

    T or F therefore the statement is TRUE.
  5. 5 ways to prove congruent triangles
    • SSS
    • SAS
    • AAS
    • ASA
    • HL (need to prove right triangles first)

    Can't use A.A.A or ASS!!
  6. Image Upload 4

    How do you find the length of the altitude in the diagram above?
    Image Upload 6
  7. Sum of Interior angles of Any Polygon
    180(number of sides-2)
  8. Sum of exterior angles in any polygon
    ALWAYS ADDS TO 360
  9. How do you find the measure of ONE EXTERIOR ANGLE of a polygon
    360/number of sides
  10. How many degrees is EACH angle in an equilateral triangle
    60 degrees
  11. What are things we know about rhombi?
    all sides CONGRUENT

    Diagonals are perpendicular

    Diagonals bisect the angles

    It is a special parallelogram
  12. What do we know about squares?
    they have all the proprties of a rectangle and a rhombus. Most importantly:

    • 90 DEGREE ANGLES
    • DIAGONALS ARE PERPENDICULAR
    • Diagonals are CONGRUENT
    • All sides are congruent
  13. How do you prove something is a TRAPEZOID on a coordinate grid?
    It has one pair of parallel sides.

    It has one pair of NON PARALLEL SIDES.
  14. What must be true about the side lenghts of a triangle...

    E.X: Which of the following lengths can create a triangle?

    a) {3,6,2}
    b) {3,6,8}
    The sum of the two smaller sides must be larger than the longest side!

    3 + 2 is less than 6 (so A wont make a triangle)

    choice B will make a triangle!
  15. What do we know about SIMILAR FIGURES?
    Corresponding ANGLES are CONGRUENT

    Ratio of sides = ratio of perimeters = ratio of altitudes

    • (Ratio of sides)2= ratio of areas
    • (ratio of sides)3= ratio of volumes
  16. HOW can you prove triangles are SIMILAR (~)
    • AA~
    • SAS~
    • SSS~

    (the S in this case meas CORRESPONDING sides are PROPORTIONAL)
  17. Angles/ Side lenghts in triangles

    Image Upload 8
    Smallest side opposite smallest angle

    Largest side opposite largest angle
  18. What is the locus of points that are a fixed distance from a point "P"?
    THINK BRAD AND HIS LIZARD ON A LEASH!!
  19. DISTANCE FORMULA
    Image Upload 10
  20. Midpoint formula
    Image Upload 12

    or

    (average the x's, average the y's)

    MAKE SURE IT MAKES SENSE BY GRAPHING IT
  21. What is an isometry?
    a transformation that PRESERVES SIZE

    the only transformation that is NOT an isometry is a Dilation!
  22. Inverse
    Negate
  23. Converse
    Flip

    (you can do FLIPS IN CONVERSE SNEAKERS)
  24. CONTRAPOSITIVE
    Logically equivalent to the original


    FLIP AND NEGATE
  25. What is a glide reflection?
    It is a transformation that combines a TRANSLATION (glide) and a REFLECTION
  26. Area of a Circle!
    A = pi*r2
  27. Area of a triangle
    Image Upload 14
  28. Area of a Trapezoid
    • Image Upload 16
    • or

    A = (average of the bases times the height)
  29. What do we know about the slopes of PARALLEL LINES?
    THEY ARE THE SAME!
  30. What do we know about the slopes of PERPENDICULAR LINES?
    negative reciprocals (flip and change sign)

    for example a line with m=2 is perpendicular to a line with a slope of m=-1/2
  31. What is the Lateral Area of a Cone or a Cylinder?
    It is the "wrapper". It does not include the bases.

    The Lateral area formulas for BOTH the cone and the Cylinder are on your reference table.


    Note: To get the complete surface area you must add on the bases.
  32. How many degrees are in ANY quadrilateral?
    360
  33. Supplementary
    Adds to 180 degrees
  34. Complimentary Angles
    adds to 90
  35. Linear Pair
    Two angles who create a line (they add to 180)
  36. What does bisect mean?
    To cut in half

    (makes two EQUAL pieces)
  37. Similar Right Triangls

    How do you find the length of the altitude in the diagram.
    Image Upload 18
    • Image Upload 20
    • Image Upload 22
    • in this case Image Upload 24
  38. How do you solve a system of equations graphically?
    • 1. Solve both equations for y.
    • 2. Graph them on your graphing calculator and use your table to graph them on the coordinate grid.
    • 3. Locate the points of intersection, circle them and then RECORD THEM!
  39. What is the locus of points equidistant from a POINT?
    THINK BRAD WITH HIS LIZARD ON THE LEASH! (it makes a circle!!!)Image Upload 26
  40. What is the locus of points equidistant from a single line?
    Two lines that run parallel to itImage Upload 28
  41. What is the locus of points equdistant from two points?
    The PERPENDICULAR BISECTOR of the segment that connects them.

    Image Upload 30
  42. What is the point of concurrency for the perpendicular bisectors of a triangle?
    Circumcenter
  43. What s the point of concurrency for the ANGLE bisectors of a tangle
    INCENTER

    this point is EQUIDISTANT from the sides of a triangle
  44. What is a median of a triangle?
    It connects the vertex of a triangle to the midpoint of the opposite side
  45. What is the Point of concurrency of the MEDIANS of a triangle
    • Centroid!
    • Important

    • Pieces are in the 2:1 Ratio
    • (2x + x = median length)
  46. What do we know about Central Angles in a circle
    Image Upload 32

    < = intercepted arc
  47. Image Upload 34
    What do we know about INSCRIBED ANGLES?
    • < = 1/2(arc)
    • Image Upload 36
  48. How do you find the valu of x in the diagram below?
    Image Upload 38
    Image Upload 40

    x = 1/2 (sum of the arcs)
  49. How do you find the measure of angles outside a circle, formed by two tangents or secats?
    Image Upload 42
  50. How do you find the measure of <1Image Upload 44
    <1 is half Arc AB

    < 1 = 65
  51. What do you know about angles in the polygon below?
    Image Upload 46
    Opposite angles add to 180

    <E + <G = 180
  52. What is the equation of a LINE?
    y = mx + b

    • Where m is the SLOPE and
    • b is the y intercept!
  53. What do we know about this picture?
    Image Upload 48
    • Image Upload 50
    • FH = DH

    • and Arc FG = Arc GD
    • and Arc ED = Arc EF
  54. What euation can we use to find the lengths of the chords in the diagram below?
    • piece*piece = piece*piece
    • Image Upload 52
  55. What equation can we use to find lenghts in this diagram?
    Image Upload 54
    External * Whole = External * Whole
  56. Identify the two congruent chords in the diagram below
    Image Upload 56
    • Arc AB = Arc CD
    • Image Upload 58
  57. What is the "Rotation Table"
    Image Upload 60

    (set up this table the second you get your test!!)
  58. How do you reflect over the line y = x
    FLIP THE X AND Y COORDINATE
  59. Exterior < theorem
    How do you find he measure of <1
    Image Upload 62
    • Image Upload 64
    • <1 = <B + <A
  60. What do we know about the length of MIDSEGMENT BE?
    Image Upload 66
    • Image Upload 68
    • BE = 1/2 (CD)

    BE || CD
  61. What do we know about midsegent GJ?
    Image Upload 70
    • Image Upload 72
    • Image Upload 74

    or GJ = Average of the bases!
  62. What are some true proportions you can set up based on this diagram Image Upload 76
    Image Upload 78Image Upload 80
Author
MissCoppola
ID
156782
Card Set
Geometry Regents Reveiw
Description
Review for the Geometry Regents
Updated

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