Geometry Regents Reveiw

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  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!
  2. Equation of a circle (MEMORIZE THISS!)
    Image Upload

    • where (h, k) is the center
    • r = radius
  3. 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.
  4. 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!!
  5. Image Upload

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

    Diagonals are perpendicular

    Diagonals bisect the angles

    It is a special parallelogram
  11. 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
  12. 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.
  13. 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!
  14. 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
  15. HOW can you prove triangles are SIMILAR (~)
    • AA~
    • SAS~
    • SSS~

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

    Image Upload
    Smallest side opposite smallest angle

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

    or

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

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

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

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


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

    A = (average of the bases times the height)
  28. What do we know about the slopes of PARALLEL LINES?
    THEY ARE THE SAME!
  29. 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
  30. 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.
  31. How many degrees are in ANY quadrilateral?
    360
  32. Supplementary
    Adds to 180 degrees
  33. Complimentary Angles
    adds to 90
  34. Linear Pair
    Two angles who create a line (they add to 180)
  35. What does bisect mean?
    To cut in half

    (makes two EQUAL pieces)
  36. Similar Right Triangls

    How do you find the length of the altitude in the diagram.
    Image Upload
    • Image Upload
    • Image Upload
    • in this case Image Upload
  37. 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!
  38. What is the locus of points equidistant from a POINT?
    THINK BRAD WITH HIS LIZARD ON THE LEASH! (it makes a circle!!!)Image Upload
  39. What is the locus of points equidistant from a single line?
    Two lines that run parallel to itImage Upload
  40. What is the locus of points equdistant from two points?
    The PERPENDICULAR BISECTOR of the segment that connects them.

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

    this point is EQUIDISTANT from the sides of a triangle
  43. What is a median of a triangle?
    It connects the vertex of a triangle to the midpoint of the opposite side
  44. 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)
  45. What do we know about Central Angles in a circle
    Image Upload

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

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

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

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

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

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

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

    BE || CD
  60. What do we know about midsegent GJ?
    Image Upload
    • Image Upload
    • Image Upload

    or GJ = Average of the bases!
  61. What are some true proportions you can set up based on this diagram Image Upload
    Image UploadImage Upload

Card Set Information

Author:
MissCoppola
ID:
156782
Filename:
Geometry Regents Reveiw
Updated:
2012-06-06 13:39:08
Tags:
Geometry Math Review
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Description:
Review for the Geometry Regents
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