CP Geometry Midterm Review Packet - hatboro- 2014-15 Date_____Block_____ Final Exam Review Packet True or False: 1 ... BEC = 24 34 ’ m AED

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Text of CP Geometry Midterm Review Packet - hatboro- 2014-15 Date_____Block_____ Final Exam Review Packet...

  • Geometry CP Name_______________________________

    Fall 2014-15 Date_______________Block____________

    Final Exam Review Packet

    True or False:

    1._______ The formula for area of a kite is 1 2.A d d

    2. ______ If two angles are equal, they are right angles.

    3. ______ A trapezoid is never a parallelogram.

    4. ______ Two points determine one and only one plane.

    5. ______ 8 cm is the radius of a circle with an area of 64 2 .cm

    6. ______ The sum of two acute angles is an obtuse angle.

    7. ______ A trapezoid may be equilateral.

    8. ______ Since the sum of 20, 30and 40 is 90, then the angles are complementary.

    9. ______ The diagonals in a rectangle are sometimes perpendicular.

    Set up and solve the following word problems.

    10. Two angles are supplementary. Find the angles if one angle is 10more than two- thirds the other angle.

    11. In a triangle, B is 12 larger than A. C is equal to the sum of the first two angles. Find the angles.

    12. ABC is isosceles and one of the base angles is 15 larger than the vertex angle. Find the angles.

    Solve the following angle problems:

    13. Find ,m CED given:

    EB bisects AED

    mAED = 74

    mBEC = 19 m CED _________________

  • 2

    A

    E D

    B

    C

    B

    I

    RD

    A

    S N

    EK

    14. Find ,m AED given:

    mAEB = 29 14

    mCED = 31 26

    mBEC = 24 34

    m AED ____________

    Draw the segment and then solve.

    15. B is the midpoint of AC . AC = x + 3

    AB = x

    16. B is between points A and C.

    AB = 4x 1

    BC = 2x + 3

    AC = 8x

    17. Given: Circle one: Congruent or Cant Prove

    If congruent, name postulate: ______________

    Finish congruence statement (only if congruent):

    _______BID

    18. Given: Circle one: Congruent or Cant Prove

    If congruent, name postulate: ______________

    Finish congruence statement (only if congruent):

    _______SAN

    AC = _____

    AB = _____

    BC = _____

    AC = _____

    AB = _____

    BC = _____

  • 3

    T

    A

    G

    O

    D

    C

    B

    A

    E

    B

    A

    C

    D

    19. Given: Circle one: Congruent or Cant Prove

    If congruent, name postulate: ______________

    Finish congruence statement (only if congruent):

    _______GTA

    20. Given: ADB CDB Circle one: Congruent or Cant Prove

    If congruent, name postulate: ______________

    Finish congruence statement (only if congruent):

    _______ABD

    21. Given: Circle one: Congruent or Cant Prove

    If congruent, name postulate: ______________

    Finish congruence statement (only if congruent):

    _______ABC

    Solve:

    22. If two lines are parallel and are cut by a transversal, two alternate interior angles represented by 3x and

    5x 70. Find the angle measures.

  • 4

    AI

    C E

    F H

    B

    D

    G

    G

    A

    C D

    F

    E

    B

    _________

    _________

    m EDG

    m DGH

    F

    BA D

    E H

    C

    G

    23. If two lines are parallel and are cut by a transversal, two corresponding angles represented by 2x + 10 and

    4x -50. Find the angle measures.

    Use the following sketch to solve:

    24. (10 8)m ABF x

    (7 10)m BFH x

    Find x = _____________ m EFB ___________ m CBD ____________

    25. Given: 32

    89

    AB CE FH

    m ABD

    m BDG

    .

    Find:

    26. Given: BF CD

    EC bisects ACD

    42m EGF Find:

    m CBF = __________

    m ABG _________

  • 5

    Simplify each radical expression

    27. 6004 28. 3

    17 29. 542964

    Solve the proportion.

    30. 4

    16 x

    x 31.

    5852

    57 x

    Are the triangles similar? If so, write a similarity statement and identify the postulate or theorem that

    justifies your answer.

    32. A D G

    C T

    O

    33. Circle one: Similar or Cant Prove

    If similar, name postulate: ____________

    Finish similarity statement (only if similar):

    _______SLP

    92

    92

    23

    68

    Circle one: Similar or Cant Prove

    If similar, name postulate: ____________

    Finish similarity statement (only if similar):

    _______CAT

  • 6

    34. Circle one: Similar or Cant Prove

    If similar, name postulate: ____________

    Finish similarity statement (only if similar):

    _______ABC

    Use the given information to determine the similar triangles. Then, solve for the missing side.

    35. Given AG YM

    GM = 5

    AG = 6

    YM = 15

    Find RM = ____

    36. Given , 2 5, 4 3 and 5 6,AB DE AB CB ED find CD.

    CD = ____________

  • 7

    37. If QPRABC ~ , m A = 30 and m B = 97, find the measures of angles Q, P, and R.

    m Q = ________

    m P = ________

    m R = ________

    38-40. Use the diagram at the right. A, B, and C are midpoints of sides GH, HJ and GJ

    respectively.

    38. If 3 8AB x and 2 24GJ x , what is AB? __________

    39. If 3 5AC y and 4 2HJ y , what is HB? __________

    40. If 7 1GH x and 4 3BC x , what is GH? __________

    41-43. Is this triangle possible?

    41. 2.5, 3.5, 5 ___________ 42. 2, 6, 9 ___________ 43. 62,13,3 ___________

    Find the third side. Write an inequality statement.

    44. 5, 15, ___________________

    Find the missing angles.

    45.

    __________

    __________

    __________

    m CAD

    m FAB

    m BCA

  • 8

    46. Find the midpoint of A(4, 7) and B(-5, 8) midpoint = ____________

    47. Find the endpoint, B, of ,AB if A(8,-4) and the midpoint is (5, -9). B = ____________

    48. Find the distance between A(2,4) and B(-12, 6). Round your answer to the d = ____________

    nearest tenth.

    49. Given the following conditional, write the converse, biconditional (if possible) and inverse statements.

    If a number is divisible by two then it is even.

    Converse: _____________________________________________________________________

    Biconditional: _________________________________________________________________

    50. Write a proof.

    Given: X is the midpoint of VY and WZ .

    Prove: VWX YZX

    Statement Reason

    1. X is the midpoint of VY and WZ 1. Given

    2. XYVX 2. _____________________________

    XZWX

    3. 3. _____________________________

    4. VWX YZX 4. _____________________________

  • 9

    51. Write a proof.

    Given: D is the midpoint of AC

    Prove: BCAB

    Statement Reason

    1. D is the midpoint of AC 1. Given

    2. DCAD 2. _____________________________

    3. BDBD 3. _____________________________

    4. ADB CDB 4. _____________________________

    5. BCAB 5. _____________________________

    52. Which of the triangles in the figure below must be isosceles?

    a) SPR

    b) SPQ

    c) QTU

    d) SQV

    53. If the hypotenuse of a 45-45-90 triangle is 5, what is the measure of the leg?

    a. 5 2

    2 b. 5 2

    c. 5 3

    3 d. 10

    54. The length of the legs of a right triangle are 4 cm and 7 cm. Find the length of the hypotenuse.

    a. 33 b. 2 13

    c. 65 d. 2 5

  • 10

    ________

    ________

    ________

    ________

    DB

    AB

    ABCm

    ECBm

    55. Use the figure at the right to determine FG.

    a. 4.2 b. 4.7

    c. 9.1 d. 23.6

    56. Find the value of x and y. Round to the nearest whole number.

    a. x = 29, y = 61 b. x = 64, y = 26

    c. x = 26, y = 64 d. x = 61, y = 29

    57. If the diagonals of a quadrilateral bisect each other at right angles, the figure is a:

    a. Rectangle b. Trapezoid c. Rhombus d. Kite

    58. Find the following measurements if 3 20WY x , 6 16ZX x , 108WPXm , WZ = 20. WXYZ is a parallelogram.

    __________

    ________

    ________

    ________

    _________

    WX

    WYXm

    WXZm

    WP

    x

    59. Find the following measurements if 144DABm and 30AC . ABCD is a rhombus.

  • 11

    ________

    ________

    ________

    ________

    DG

    EH

    FHGm

    DEGm

    60. Find the following measurements in simplest radical form if 214DF . DEFG is a square.

    61. A trapezoid has midsegment of 13 and one base of 21. Find the other base.

    b = ______________

    62. A trapezoid has midsegment of (2x+4) and bases (3x+2) and (2x+1). Solve for x.

    x = ______________

    63. Given kite ABCD, BE = 12, BC = 20 and the 105m ABC and the 85 ,m DAB find the indicated

    measures.

    ___________m DCB

    EC = _____