Name _____ - Download as DOC by HC111204001111

VIEWS: 23 PAGES: 14

									Name _____________________________          Date ___________________

                       Review ~ Pre AP Geometry Midterm 2010
 Vocabulary is on the test, you need to know all, so if you see one you don’t
remember or think you need review on, especially formulas, postulates or theorems
we haven’t seen in a while, please make sure to review the concept.
Vocabulary:
Undefined terms                 Conditional statement           Scalene triangle
Point                           Converse                        Isosceles triangle
Line                            Inverse                         Triangle sum theorem
Plane                           Contrapositive                  Exterior angle theorem
Collinear                       Hypothesis                      Third angles theorem
Coplanar                        Conclusion                      CPCTC
Noncollinear                    Law of detachment               SSS
Noncoplanar                     Law of syllogism                SAS
Segment                         Biconditional statement         ASA
Endpoint                        Postulate                       AAS
Ray                             Theorem                         HL
Opposite rays                   Counterexample                  Included side / angle
Postulate                       Algebraic properties            Isosceles triangle
Postulates (chapter 1)          from chapter 2                  properties/theorems
Distance formula                Proof                           Perpendicular bisectors
Congruent                       Two column proof                Angle bisectors
Midpoint (definition            Parallel lines (and it’s        Medians
and formula)                    slope)                          Altitudes
Bisect                          Perpendicular lines             Circumcenter
Segment bisector                (slope)                         Incenter
Segment addition                Skew lines                      Centroid
postulate                       Transversal                     Orthocenter
Angle addition                  Corresponding angles            Triangle midsegment
postulate                       Alternate interior angles       theorem
Angle                           Alternate exterior              Equidistant
Vertex                          angles                          Point of concurrency
Acute angle / triangle          Same side interior              Triangle inequality
Right angle / triangle          angles                          theorem
Obtuse angle / triangle         Slope (formula)                 Hinge theorem and it’s
Straight angle                  Coinciding lines                converse
Angle bisector                  Point slope form                Pythagorean theorem
Adjacent angles                 Slope intercept form            Converse of the
Linear pair                     Vertical lines (equation        Pythagorean theorem
Complementary angles            and it’s slope)                 Pythagorean triple
Supplementary angles            Horizontal lines                45-45-90
Vertical angles                 (equation and it’s slope)       30-60-90
Inductive reasoning             Equiangular triangle            Angle side relationships
Deductive reasoning             Equilateral triangle            in triangles pg 333
Refer to the figure below to name each of the following. Use appropriate symbols where necessary.
 1.__________              The intersection of M and L.
                                                                            L
 2.__________             A ray opposite DB.                                     B
 3.__________              A plane containing CE.                      C
                                                                                  E
 4.__________              The intersection of L and CE.        M           D
 5. _________                      Three collinear points                                   A
 6. _________                      Three coplanar points
____       7.    Find AC.

                                      A                          B             C        D
                              –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

____       8.    D is between C and E.         =     ,       =       , and DE = 27. Find CE.

       C        4x + 8         D    27    E

                         6x

____       9.    B is between A and C. AC = 24 and BC = 11. Find AB.

                                                                     L
_____ 10. What are three names for the angle?

                                                         1               N
                                                   M


______11. If                  and                  then what is the measure of              The diagram is not to scale.




                                                   mWXY  88  ; mWXZ  4 x  3  ; mZXY  2 x  1
                                                                                                                  
______ 12.
                 Solve for x:                                                          W
                                                                                                    Z


                                                                     X
_____ 13. Find the measures of two complementary angles, A & B, if mA = (7x + 4)Y mB = (4x + 9).
                                                                                    and


_____ 14. Find the distance between the points E(-3, -4) and F(5, 4). Simplify the radical if necessary.


_____ 15. Find the midpoint of the segment with the given endpoints. (-7, 7) and (-9, 8)


_____ 16. The complement of a 35 angle is an angle with a measure of:


_____ 17. The supplement of a 25 angle is an angle with a measure of:
In the diagram, name the / a pair of

 ________18.    adjacent angles.

 ________19.    Name a linear pair:
                                                                                      1 2 3
 ________20.    Vertical angles                                                       5 4




_____ 21. M is the midpoint of AB. AM = 9x – 6 and BM = 6x + 27
        Find:
                 X=                  AM =                   BM =

_______22.     bisects                            and                          Solve for x and find
                         The diagram is not to scale.




23. How a line and a line are segment the same? How are they different?
_______________________________________________________________________
24. How are angles classified? Give an example of each.
________________________________________________________________________
25. What are the building blocks of geometry?
________________________________________________________________________
26. How are Supplementary angles and a linear pair the same? Different?
    ________________________________________________________________________

Draw, label and show the notation for each of the following:
   27. A line segment with endpoints C and D.

   28. A line containing X and Y

   29. A ray with endpoint M that passes through P.


       Given the diagram:

       30) Name the type of angles:
       __________________________                      y
                                                           bx  26g
                                                           2                  bx  14g
                                                                               5      


       31) Solve for x and y
  KNOW: All Properties of equality and congruence pgs 104 and 106.

      32. Conditionals are known as ______________________________________.

      33. What is a conjecture? _____________________________________

      34. Inductive reasoning is based on __________________________ and deductive reasoning is
          __________________________________________________.

      35. A counterexample invalidates a statement.      TRUE       FALSE

      36. Write the negation of: Points on the same plane are coplanar.
          _____________________________________________________

      37. When a conditional and its converse are true you can combine them as a ______________________________.


  Write a conditional statement for the situation described, then write its converse, inverse, and
  contrapositive.
                                     Parallel lines do not intersect.

Underline the hypothesis once, and the conclusion twice.
  38. Conditional:


   39. Converse:


   40. Inverse:


   41. Contrapositive:

If possible, write the biconditional statement, if not tell why.
41. Every isosceles triangle has two congruent sides.


  42. Use the Law of Syllogism to draw a conclusion from the two given statements.
  If you exercise regularly, you have a healthy body.
  If you have a healthy body, you have more energy.
  ______________________________________________________________________
  ______________________________________________________________________

  43. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not
  possible.
  I will score well on the exam if I study for 1 hour each day.
  I will score well on the exam.
  ______________________________________________________________________

  44. Find the missing elements in the sequence below.
         2, 5, 10, 17, 26, 37 ,   , 65, 82 ,        , 122, . . .
45. Find the values of x and y.                                          46. Identify the transversal and classify the angle
                                                                         pair     and .

                                                                                           n            m
          3y°                                                                                       2
                 126°                                                                           1       3
      3x – 6°                                                                                       4



                                                                                                              9    10
                                                                                            5   6                 12    11
      Drawing not to scale                                                l
                                                                                           8    7




Name the indicate angles
                                                                                           1 8
    47. 4 and 5_____________
                                                                                          2 7
    48. 2 and 3_____________
    49. 1 and 7_____________                                                    3 6
    50. 6 and 8_____________                                                   4 5
    51. 1 and 5_____________
    52. 2 and 6_____________
.
If p q , then find the value of x.

53.                                                            54.
                                                                                                        (4x)
      p                       (6x)
                                                                     p

      q                      (3x)                                   q                              (2x + 30)



55. Name all the angles if m5 = 120                                56. Find the values of x and y. The diagram is not to
                                                                     scale.


                    1 2
                                      p
                   4 3
                                                                                         41°
                                                                              (x – 3)°      (y + 8)°
                 56                                                                                     74°
                                      q
                7 8
                         pq
Determine whether             and     are parallel, perpendicular, or neither.

57.
Write the equation of a line that has:

58. slope –2; passes through ( 3, 5 )           __________________________________


59. Find the slope of line given these two points (0, 7), (1, 9). _____________________


      And write the equation of the line: ________________________


60. Graph 3x – 7y = 14                          61. Graph y = -9




Write equations for the line that are parallel and perpendicular to the given line and that passes through the given
point.

            3
62.      y = x – 9; (–8, –18)
            4



63. Know how to classify triangles by sides and by angles:



                                                                            40
64.x = _______                                         65.x= ________
                                x                                          

                                                                               x               155
                      52                 35                                                     
                                        

                                                                                    38°
66.x=______                                            67. x=______
                            80                            y= ______                      19°
                                                           z=______
                                        (3x -22)                           56°
                       x                                                                  x°   z°    y°
68. In the diagram:
                                         C                            D
List the six congruent parts:

                                                       F

                                A                 B
                                                                     E
69. Write a congruence statement for the given triangles. ___________________________________

70. ADC  BDC by: _______                            71. These triangles are congruent by: _________
                                                       Finish the congruence statement:
                C




      A         D          B




72. These triangles are congruent by: _______          73. These triangles are congruent by: _______




74. These triangles are congruent by: _______          75. These triangles are congruent by: _______




76. What is the difference between ASA and AAS? __________________________

77. What does CPCTC stand for?
________________________________________________________________________________________________________________

78. If BCDE is congruent to OPQR, then        is congruent to


79. One of the acute angles in a right triangle has a measure of         . What is the measure of the other acute angle?
80. Use the information in the figure. Find                    81. Find m          , given            ,             , and
m             .
                                                                                    B                     E
                          E


                      |

                                                                             A     D                      C     F

           |   116°
D                     F

 Drawing not to scale




Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. And if so what kind of triangle.
Explain.

82. 3, 9, 10                                                   83. 40, 9 , 41

84. 4, 8, 14                                                   85. 7, 20, 23

86. Determine whether the set of numbers can be the measures of the sides of a right triangle. Then state whether
they form a Pythagorean Triple.
10, 24, 26

Simplify the radical expression.

87.                                                            88.


89. 8 3        75                                             90.    3 (4 5  6 3 )

Simplify the radical expression by rationalizing the denominator.


91.                                          92.                                                   93.




94.      Find x.                                               95. Find n.
                                                                                              6


                          37
           x                                                                            6 2               n




                      15
96.Find the value of x. The diagram is not to scale.                        97.List the sides in order from shortest to longest.
                                                                            The diagram is not to scale.
                                                                                                    J
                             40
                                                                                                           66°

                                                                                                                             50°   K

         x                                             40
                                               32
                                                                                                                   64°

                                  25                        25                                                     L


98. Find the values of x, y, and z.                                  99. Find x and y.
                                                                                   K
                     N


                                                                                                y
              29°
                     31°
                                                                             3 in.

                                                                                                    45°
                                                                               J             x                 M


  62°            x       y                 z
 M                   P                         O
100. The hypotenuse of an isosceles right triangle is 6 inches. Find the area.

101. Find the values of x and y.                                            102. Find y.
                              N                                                                           N

             x                                     22 mm
                                                                                       y
        45°                                             30°                            45°
 M                                 y                             P
                                                                                   M                    5 ft             P

103. Find x and y. Write all radicals in simplest form.                     104. What is the perimeter and area of the triangle?
                                                                            (Round to the nearest decimal place.)
                                                                                                 N
                                               C

                     x                              y
                                                                                        6 in.
        30
 A                           6 3 ft                     B
                                                                                                                             30

                                                                                             M                                         L
105. Points B, D, and F are midpoints of the sides of                   EC = 39 and DF = 17. Find AC. The diagram is not to scale.
                                                   A




                                                            B
                                       F




                                                                 C
                                                   D
                              E
106. For a triangle, list the respective names of the points of concurrency of
• perpendicular bisectors of the sides
• bisectors of the angles
• medians
• lines containing the altitudes

107. In ABC, G is the centroid and BE = 9. Find BG and                         108.
GE.
                C                                                                                   C




                                                                                           X                Z



       B                    D
                    G                                                                  A                Y       B




                                                                                Name an altitude in the given triangle.
A               F               E
                                                                                       _______________
                                                                                Name a median in the given triangle.
                                                                                       _______________




109. Find the length of                 , given that     is a median of the triangle and AC = 40.
                D




           A                B       C

109.


                        R           X              S




                                    T


If X is the midpoint of             , then        is called a(n) ________________ of           .

If TX is on the perpendicular bisector of                 , then TX is equidistant from _____ and _____.

If               , then         is called a(n) ________________ of              .

If         is the bisector of              then ______     ______
                                                                        A
Proofs:
                                                                       3 4
1.      Given: AB  AC, X is the midpoint of BC

      Prove: ABX  ACX
                                                                      1 2
                                                           B               X
      Proof:                                                                       C
                  Statements                        Reasons




2.    Given: Given B is in the interior of  AOC
                                                   (2x)°
        and
      Prove: m BOC = 108                                     6(x – 3)°


                                                   Drawing not to scale
      Proof:
                  Statements                        Reasons




                                                                                        A

                                                                                       3 4

3.    Given: AX  BC, X is the midpoint of BC

      Prove: ABX  ACX
                                                                                       1 2
                                                                               B
      Proof:                                                                            X
                                                                                             C
                  Statements                        Reasons
4.       Given: AB II DE, AB  DE

         Prove: ABC  EDC

         Proof:
                        Statements           Reasons




                                                              B
5.       Given: DCA  BCA, B  D
         Prove: AB  AD
                                                          C       A



         Proof:                                               D
                        Statements           Reasons




                                                  q

                                               1 2
6. State the reasons in this proof.           3 4
                                                      p


     Given:                                 5 6
                                                      r
     Prove:                             7    8


Proof:
                  Statements           Reasons
                                                              1
                                                          3       l
7. Given:
Prove:
                                                     2
                                                                  m


Proof:
                  Statements                        Reasons




                                                                          B


                                                                      C       A
8.       Given:
         Prove:
                                                                          D

         Proof:
                      Statements                         Reasons




9. Given:  B and  D are right angles, C is the midpoint of AE

         Prove: C is the midpoint of BD

         Proof:
                      Statements                         Reasons
                                                                                A

10. Given: 1  2, X is the midpoint of BC                                 3 4


      Prove: AX bisects BAC

      Proof:                                                                1       2
                 Statements                          Reasons        B           X
                                                                                            C




                                                                                    B




11. Given: ABC is isosceles, with base AC,  FGD  IHD, BD  AC
       Prove: AEC is isosceles
       Proof:                                                           A           D   C
                  Statements                           Reasons

								
To top