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

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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 = _____