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Geometry Study Guide- Sample Questions by donovantatehe

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									                        Geometry Study Guide- Sample Questions

Unit 1: Tools of Geometry
Sample Questions:

                      Name the Property (example: associative property of multiplication)

   1) 1 · 19 = 19                                                4) 11 + 0 = 11
   2) -2/5 · 20/-8 = 1                                           5) (3 · -17) · -13 = 3 · (-17 · -13)
   3) -14 · 11 is an integer.
                                   Name the Property (example: Symmetric)

   6) If 4 = -7H -9 and -7H -9 = -15T -7 then 4 = -15T -7.
   7) If 13T -15 = 11S -2 and 11S -2 = -14T + 18 then 13T -15 = -14T + 18.
   8) If 6Q -13 = -5L + 1 then 6Q -19 = -5L -5.
   9) 3 = 3
   10) If 3F -7 = 16M -12 then (8S)(3F -7)= (8S)(16M -12).
   11) L, D, P, and U are collinear with L between D and U, and P between L and U. If UP = 13x -19, LP = 7x -13, DU
       = x + 291, and LD = 9x + 15, solve for x.
   12) Q, J, and K are collinear with J between K and Q. If JQ = 4x + 16, QK = 5x + 225, and JK = 12x + 11, solve
       for x
   13) S, N, T, and G are collinear with G between T and N, and S between G and T. If TN = -20x + 136, ST = 18x +
       4, NG = 11x -20, and GS = 18x + 18, solve for x
   14) P, N, and M are collinear with P between N and M. If PM = 2x + 18, NM = 14x + 56, and PN = 18x + 2, solve
       for x
   15) B, R, and H are collinear with H between R and B. If RB = 17x + 69, BH = 14x + 9, and HR = 8x, solve for x
   16) G is in the interior of YEU. If m GEY = (4x + 14)°, m YEU = (18x -60)°, and m GEU = (x + 17)°, solve
       for x
   17) A is in the interior of YFM, and T is in the interior of AFM. If m MFT = (8x + 8)°, m AFT = (14x +
       8)°, m YFM = (-2x + 237)°, and m AFY = (18x + 11)°, solve for x
   18) E is in the interior of GCF. If m ECG = (x + 19)°, m GCF = (16x + 19)°, and m ECF = (5x + 10)°, solve for
       x
   19) S is in the interior of JRD. If m SRD = (4x + 1)°, m JRD = (10x + 67)°, and m SRJ = (12x + 6)°, solve
       for x
   20) H is in the interior of BZU. If m HZU = (x + 9)°, m BZU = (19x -51)°, and m HZB = (8x)°, solve for x
Mark the statement as Always, Sometimes, or Never True
   21) Through any three distinct points there exists exactly one line.
   22) A line contains at least two points.
   23) If two distinct lines intersect, then their intersection is a plane.
   24) Through any two distinct points there exists exactly one line.
   25) Through any distinct point there exists exactly one line.



Unit 2: Logic

   26) Write the contrapositive: It is 1:00 pm given that Harry woke up early.
   27) Write the inverse: Ann is not married assuming that the pen is not blue.
   28) Write the inverse: If Opal likes surfing the web then Gabrielle likes candy.
   29) Write the inverse: If Wendy did not go out Tuesday night then Harry doesn't go to the store.
   30) Write the inverse: Alexis loves school given that Val was not playing games.
   31) Write the converse: George likes peanuts assuming that the project is due Monday.
   32) Write the inverse: If apples are not on sale then Marlene has a red hat.
   33) Write the contrapositive: If Adrian likes football then the dog needs to go out.
   34) Write the inverse: Apples are on sale assuming that the cat is not white.
   35) Write the inverse: Apples are not on sale only if today is Friday.
   36) Write a counterexample: If Xavier does not have a red hat then Ann loves school.
   37) Write a counterexample: If Wendy does homework after dinner then Lenny doesn't go to the store.
   38) Write a counterexample: If Zelexis did not go to the store then Noah doesn't like peanuts.
   39) Write a counterexample: If the pen is blue then the project is not due Sunday.
   40) Write a counterexample: If Rebecca is not married then the dog needs to go out.
Translate into symbolic form:
   41) Today is Wednesday and the cat is white.
   42) The project is due Wednesday if and only if it is 1:00 pm.
   43) Alexis did not go out Sunday night or frogs do not like snow.
   44) If the project is not due Tuesday and yesterday was Friday then Dever likes football.
   45) If the dog needs to go out or Val did not go to the store then Dever is in 10th grade.

                                                     Translate:

    46) Let p = Gabrielle likes peanuts. Let q = Nina likes surfing the web. Let r = today is Friday.If p → q and q →
        r then p → r.
    47) Let p = the project is due Sunday. Let q = Charlie likes surfing the web. p → q
    48) Let p = Wendy woke up early. Let r = apples are on sale. p ↔ r
    49) Let p = it is raining. Let q = Tulip has a red hat.~p → ~q
    50) Let p = Noah is in 10th grade. Let q = the pen is blue. p ↔ ~q

                 Combine the statements using the Law of Syllogism or the Law of Detachment:

    51) If Pierce doesn't like peanuts then Barbara has a red hat. Pierce doesn't like peanuts.
    52) Zelexis went out Sunday night. If the cat is not white then Zelexis did not go out Sunday night.
    53) It is raining. If it is not raining then Ian did not go to the store.
    54) If Eugene doesn't like candy then Jamie doesn't like football. If Cathy did not wake up early then Jamie
        likes football.
    55) If the project is not due Wednesday then Dever goes to the store. The project is not due Wednesday.

Unit 2: Parallel Lines

                                                       Solve:

1) Write the equation of a line parallel to y = 13x going through (2,-2)
2) Write the equation of a line parallel to y = -8x -7 going through (-2,-3)
3) Write the equation of a line parallel to y = -5x + 11 going through (2,1)
4) Write the equation of a line parallel to y = -12x + 3 going through (0,-5)
5) Write the equation of a line parallel to y = -15x -10 going through (3,-3)
6) Write the equation of a line perpendicular to y = -20x -5 going through (1,2)
7) Write the equation of a line perpendicular to y = -7x -9 going through (-1,4)
8) Write the equation of a line perpendicular to y = 13x + 9 going through (-1,1)
9) Write the equation of a line perpendicular to y = -9x -2 going through (-3,-5)
10) Write the equation of a line perpendicular to y = 4x -14 going through (-5,-2)

                                                       Solve:
16) Find the distance between (13,19) and (-7,16)
17) Find the distance between (-6,-13) and (2,-19)
18) Find the measure of the line segment going from (-10,7) to (15,-2)
19) Find the measure of the line segment going from (11,-13) to (19,9)
20) Given F = (-15,19) and A = (-7,16), find FA
21) (7,-18) is the midpoint between (5,15) and another point. Find the other point.
22) B is the midpoint between V and E. V = (-18,12), E = (-7,-14). Find B
23) Bisect the segment from (-10,9) to (-9,8)
24) (15,19) is the midpoint between (-17,-5) and another point. Find the other point.
25) (12,15) is the midpoint between (18,5) and another point. Find the other point.
26) Find the slope of a line parallel to the line that goes through (-1,-20) and (-12,19)
27) Find the slope of a line parallel to the line that goes through (-19,18) and (-17,-8)
28) Find the slope of the line containing (-1,-11) and (1,-20)
29) Find the slope of a line parallel to the line that goes through (4,-17) and (-12,8)
30) Find the slope of a line parallel to the line that goes through (-12,-10) and (-11,-16)

Unit 3: Transversals




    56)




    57) Name the relationship:     4 and    12)




    58) Name the relationship:     6 and    8
    59) Name the relationship:     5 and    1
60) Name the relationship:      1 and   4




Solve:




61)
      This drawing shows an apparatus designed to divert light rays around an obstacle. The light comes in on
      line m, reflects off of line a, then reflects off of line b and ends up on line n. a // b and m // n.
      Furthermore, because the angle of incident equals the angle of reflection, 2             4 and 7      10. m 5
      = 156°, what is m 8?




62)
      If m // p, and m 7 = 31°, what is m 1?
   63)
         If r // t, what is the relationship between m 4 and m 8?




   64)
         If c // d, what is the relationship between m 16 and m 13?

Unit 4: Triangle and Polygon Angle Measures

                                                         Solve:

   65)     B and      W are congruent. m B = 39°. What is m W?
   66)     U and      G are supplementary. m U = 56°. What is m G?
   67)     B and      U are congruent. m B = 57°. What is m U?
   68)     G and      D are complementary. m G = 77°. What is m D?
   69)     V and      G are congruent. m V = 20°. What is m G?

                                                       Solve for x:
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   70)
   (19x -15)°         (x + 8)°
                                                                        (19x -17)°



   71)
   (13x -8)°       (3x + 2)°                                          74)
                                                                  (11x + 2)°       (3x +5)°




          72) (5x -1)°

                                                                      75)
             (4x + 13)°                                                     (17x -12)°
   73)
         (11x -14)°
      (13x + 14)°

76)

      (4x -3)°



                                                    Solve:

77) In     QRD, m    Q = 25°, m D = 20°. What is m R?
78) In     LTK, m   L = -6x + 172, m K = -2x + 90, and m T = -17x + 343. What is x?
79) In     VPA, m   V = 2x + 58, m P = -12x + 153, and m A = -12x + 145. What is x?
80) In     AST, m   A = 2x + 75, m S = -11x + 151, and m T = 4x + 19. What is m T?
81) In     QEB, m    E = 2x -3, m Q = -5x + 18, and m B = -6x + 183. What is m E?




82)                                                          85)
      m L = (2x + 4)°, m P = (9x -6)°, and m SAL                   m L = (x + 20)°, m P = (x + 13)°, and m SAL
      = (x + 78)°. Solve for x.                                    = (-5x + 138)°. What is m SAL?




                                                             86)
83)                                                                m P = (x + 13)°, m N = (x + 5)°, and m SIP
      m L = (x + 7)°, m P = (x + 15)°, and m SAL                   = (14x -198)°. Solve for x.
      = (-11x + 126)°. What is m L?




                                                             87)
                                                                   m BOR = 4°, m BRO = 13°, and m
                                                                   MDO=16°. Find the measures of all the other
                                                                   angles.




84)
      m N = (x + 18)°, m P = (x + 11)°, and m SIP
      = (-11x + 185)°. What is m P?
                                                     94)
   88)
                                                           m ALP = (-13x -13)°, m P = (14x -14)°, and
           CAT has   A     C. Find m A.
                                                           m SAL = (-7x -10)°. Find x.




   89)
                                                     95)
           KID     MID, KDI       MDI, m MDK =
                                                           m KID = 24°, m KDI = 7°, m MDI = 60°,
         320°, and m DMI = 144°. Find m DKI.
                                                           and m DMI = 93°. Find all the remaining
                                                           angles.




   90)                                               96)
         m WFR = 110°, m PRF = 29°. Find m RAW.            m P = (-2x + 4)°, m N = (-6x + 16)°, and m
                                                           SIP = (-6x + 18)°. Find x.

                                                     Name the Postulate or Theorem Used to Prove
                                                     the Triangles Congruent (if any):

                                                     97) Given:
   91)
         m WFR = 115°, m PRF = 7°. Find m RAW.

Unit 5: Triangle Congruence




   92)
          JAY has m J = 74° and     A     Y. Find
                                                     98) Given:
         m Y.




   93)
         m P = (-20x -18)°, m N = (2x + 6)°, and m
         SIP = (-13x + 11)°. Find x.
                                       110)         Given:
   106)
      Given:




                                    __ __
                                    AP AG,    RAP       GAP,   RPA   G

   107)         Given:
                                    Prove:   BAG     RAP. 13)
                                        111)     Given:




   108)        Given:                 __   __ __ __
                                    13. BR BT, TA AR


                                    Prove:    BAR       BAT.




                                       112)         Given:




                   Write a Proof:

   109)        Given:

                                    __ __ __ __
                                    RY LY , RP LP


                                    Prove:    PRY      PLY.



__ __ __ __
OC IP , CW GP ,         C   P


Prove:    COW       PIG.
  113)           Given:                                              116)           Given:




                                                                  __ __
         T       D,       TSA     DSA                             YB YS,      O      A,      B        S

     Prove:           SAT       SAD.
                                                                  Prove:
                                                                            __
  114)           Given:
                                                                  Y bisects BS

                                                                     117)           Given:




__ __
BA MA,       B     M

Prove:
__ __
MN BT

  115)           Given:                                                    Prove:     A          S.

                                                                     118)           Given:




       RBA            TBA,      RAB     TAB
     Prove:           RAT is isosceles.
                                                                             RAB      TAB,      RBA     TBA
                                                                           Prove:     RAT is isosceles.
                                                         Solve:

  119)           Given two sides of a triangle: 11 and 9, what is the range of possible lengths for the 3rd side?
  120)           Given two sides of a triangle: 4 and 18, what is the range of possible lengths for the 3rd side?
  121)           Can we make a triangle with side lengths: 8, 13, and 14?
  122)           Given two sides of a triangle: 5 and 20, what is the range of possible lengths for the 3rd side?
  123)           Can we make a triangle with side lengths: 6, 20, and 1?
124)
   m W = 52° and m M = 53°. Order the sides from smallest to largest.




125)
126)       m B = 19° and m I = 16°. Order the sides from smallest to largest.




127)
   CL = 11, SL = 23, and CS = 13. Order the angles from smallest to largest.




128)
   TS = 11, BS = 24, and TB = 26. Order the angles from smallest to largest.




129)
   m W = 35° and m M = 25°. Order the sides from largest to smallest.
130)
   Stranded on an island, a man relaxing by a tree spots a rescue plane. The plane is directly over a buoy. The
   island, plane, and buoy make a triangle. (Aren't you surprised?!) The angle at the island is 13° and the angle
   at the plane is 14°. Order the sides of the triangle from smallest to largest.




131)
   Warren, Betty, and Maude are best friends who all live in the same town. Their houses make a triangle (as
   shown).The distance from Maude's house to Betty's house is 16, the distance between Warren and Betty's
   homes is 14, and distance from Maude's home to Warren's home is 39. Order the angles of the triangle
   from smallest to largest.




132)
   A child cut faces into three pumpkins, and then put them back into the pumpkin patch. Someone later found
   these pumpkins and noticed that they were arranged in a very interesting triangle. He named the pumpkins:
   Smiley, Joking, and Perturbed. The angle at Perturbed is 52° and the angle at Joking is 53°.
   Order the sides of the triangle from largest to smallest.
   133)
      Off a high cliff, there is a lighthouse. Two ships are approaching the lighthouse, when they spot the light.
      The Catamaran and the Sailboat form a triangle with the lighthouse. The distance between the boats is 32,
      the distance from the light at the top of the lighthouse to the Sailboat is 30, and distance from the light
      at the top of the lighthouse to the Catamaran is 29. Order the angles of the triangle from smallest to
      largest.




   134)
      A tilting tree casts a shadow across the ground. The base of the tree, top of the tree, and the end of the
      shadow make a triangle. The angle at the base of the tree is 51° and the angle at the top of the tree is 57°.
      Order the sides of the triangle from largest to smallest.

Unit 6: Right Angle Triangles
    135)       10 and 15 are two sides of a right triangle. What are the two possibilities for the third side?
    136)       Find two Pythagorean triples with 5 as one of the numbers.
    137)       5 and 12 are the lengths of the legs of a right triangle. What is the length of the hypotenuse?
    138)       4 and 12 are two sides of a right triangle. What are the two possibilities for the third side?
    139)       Do 24, 10, and 26 form a Pythagorean triple?

                                       Solve (round to two decimal places):




   140)                                                          141)
      RT = 6, TP = 8. Find ST.                                      RP = 12, TP = 9. Find SP.
142)
   DO = 3, OW = 11. Find NO.    147)
                                   MR = 4. Find OM and OR




143)
   JA = 4, AC = 9. Find KC.     148)
                                   SQRE is a Square. QE = 10. Find RQ and RE




144)
   ST = 16, IS = 11. Find AS.

                                149)
Solve:
                                   BA = 5. Find TA and BT




145)
   MO = 9. Find RO and MR




                                150)
                                   XY = 15, ZX = 36, and YZ = 39. Find cos Z.




146)
   ST = 5. Find RS and RT
                                                    156)
151)
                                                       JL = 15 and m K = 82°. Find KL.
   ZX = 12, XY = 9, and YZ = 15. Find sin Y.




                                                    157)
152)
                                                       GD = 15 and m D = 13°. Find GF.
   GF = 8, DF = 6, and GD = 10. Find tan D.




153)
     S is a right angle. ST = 3, SR = 4, and TR =
   5. Find tan R.


                                                    158)
                                                       DF = 25 and m G = 62°. Find GD.




154)
     S is a right angle. SR = 8, ST = 6, and TR =
   10. Find tan T.
                                                    159)
Solve (Round to two decimal places):                   b = 10 and m A = 53°. Find a.




155)
   GF = 21 and m G = 64°. Find DF.
160)                                               163)
   XY = 21 and ZX = 12. Find m Y                      YZ = 12 and XY = 6. Find m Z




161)
    S is a right angle. ST = 7 and TR = 10. Find
   m T


                                                   164)
                                                      JK = 10 and JL = 7. Find m J




162)
   GF = 5 and GD = 7. Find m D

								
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