Name: ____________________________________ 6/2010

Teacher (circle one) Gordon King

Geometry Level 2 Final Exam 2010

Lexington High School Mathematics Department

This is a 90-minute exam, but you will be allowed to work for up to 120 minutes. Calculator use is

permitted for the entire exam.

There is a reference sheet that you may use at any point during the exam. This sheet is separate from

the exam, and is green.

A separate word bank is not provided, but the multiple choice questions and options contain all

vocabulary need for other test questions.

The exam has 4 parts. Point values for each part appear below.

In total, there are 100 points that you can earn. The course faculty will set a letter grade scale after the

tests have been graded.

Sections Points Earned (for teacher use only)

Part I. Multiple Choice

1 point each, 15 questions ___________ / 15

Part II. Short Answer

2 points each, 10 questions ___________ / 20

Part III. Long Answer

Points are as marked on the test, 10 questions ___________ / 41

Part IV. Explain What is Wrong

3 points each, 8 questions ___________ / 24

Total Points Earned ___________ / 100

Exam Grade

Teacher use only:

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12

Level 2 Geometry Final Exam 2010 Page 1

Name: ___________________________ Teacher:Gordon King

Part I. Multiple Choice

Directions: Choose the best answer to each question. Write your selection on the line provided.

_____ 1. Three points that lie on the same line are:

a) coplanar

b) collinear

c) non-collinear

d) intersecting

_____ 2. Two lines in the same plane that never touch are:

a) perpendicular

b) collinear

c) skew

d) parallel

_____ 3. 1 and 8 are:

a) alternate exterior angles

b) alternate interior angles

c) vertical angles

d) same-side interior angles

_____4. AOC is

a) an obtuse angle

b) a right angles

c) an acute angles

d) a straight angle

87

65

43

21

C

A

O

D

Level 2 Geometry Final Exam 2010 Page 2

_____ 5. Which statement is true about the solid shown?

a) The solid is a pyramid with a square base

b) The solid is a pyramid with a triangular base

c) The solid is a prism with a square base

d) The solid is a prism with a triangular base

_____ 6. Find the intersection of

AB and

BA

a)

AC

b)

AB

c) B

d)

AC

_____ 7. Classify ABC by both its angles and its sides.

a) Acute and equilateral

b) Acute and isosceles

c) Obtuse and scalene

d) Obtuse and isosceles

_____ 8. Chose the side that is included between G and H.

a)

HJ

b)

JG

c)

GH

d) none of the above

_____ 9. Chose the angle that is included between

HJ and

JG.

a) J

b) H

c) G

d) none of the above

A CB

35°A C

B

GH

J

GH

J

Level 2 Geometry Final Exam 2010 Page 3

E

F

D

A

C

B

DA B

C

_____ 10. Choose a congruence statement for the triangles shown.

a) CBA FED

b) ABC DFE

c) CBA EFD

d) BCA DFE

_____ 11.

CD is a(n)

a) Angle bisector

b) Linear bisector

c) Perpendicular bisector

d) Midpoint

_____ 12. The transformation that means “slide” is:

a) rotation

b) dilation

c) reflection

d) translation

_____ 13. Which of the polygons below is a regular polygon?

a) rectangle

b) rhombus

c) trapezoid

d) square

_____ 14. A quadrilateral with exactly one pair of sides parallel is a _________.

a) parallelogram

b) kite

c) trapezoid

d) square

Level 2 Geometry Final Exam 2010 Page 4

_____15.

EG is a(n)

e) Angle bisector

f) Linear bisector

g) Perpendicular bisector

h) Midpoint

E

H

F

G

Level 2 Geometry Final Exam 2010 Page 5

Part II. Short Answer

Directions: Write the answer to each question in the space provided. Do not forget to include

appropriate units for some problems that use specific units (for example: 3 in, 5 cm3, 12 ft

2)

Questions Answers

16.

BC bisects ABD. Find mABD

mABD = ___________

17. Find the area of the figure below.

Area = ______________

18.ABD is complementary with EBC. Find mDBE.

50°

A C

E

B

D

mDBE = ___________

40°B

A

D

C

Level 2 Geometry Final Exam 2010 Page 6

19. State the reason that ABC DEF.

E

F DA

C

B

_________________

20. Calculate the surface area of the solid.

SA = _________________

21. Name the type of transformation shown below.

__________________

22. Name the type of transformation shown below.

__________________

2 feet

8 feet

3.5 feet

feet

Level 2 Geometry Final Exam 2010 Page 7

56°35°D F

E

23. True or false: PRQ is similar to STU.

59°

64°

57°

57°Q

R

P S

TU

(circle one)

True or False

24. Classify DEF by both its angles and its sides.

_________________

_________________

25. Find the union of

AB and

BC

A CB

ABBC ___________

Level 2 Geometry Final Exam 2010 Page 8

Part III. Long Answer

Directions: Read each question carefully, and be sure to answer all parts. Write your answers in the

spaces provided. Full credit will be given for correct answers with work shown. Work that is

partially correct may receive partial credit. Do not forget to include appropriate units for some

problems that use specific units (for example: 3 in, 5 cm3, 12 ft

2).

26. (5 pts) Solve for x then solve for y. Show all work.

x = ____________

y = ____________

27. (4 pts) The volume of the cone is 160 m3. The height is 17cm. Find the radius. Show all work.

Round your answers to the nearest tenth when necessary.

r = __________

y°

5x + 10 °

3x + 60 °

r

hl

17 cm

Level 2 Geometry Final Exam 2010 Page 9

82°

3x - 6 °5x °

JL

K

28. (5 pts) Use JKL to answer each part.

a. Solve for x. Show your work.

x = ___________

b. Use your answer from part a) to find the measurement of each angle in JKL.

mJ = ___________

mL = ___________

29. (5 pts) Suppose

D is a right angle.

a. Find the interior angle sum of pentagon ABCDE. Show all work.

interior angle sum of ABCDE = ______________

b. Solve for x and find the measure of

A . Show all work.

x = _________________ mA = _________________

116°

3x-19 °

3x-31 °

2x-16 °

E

D

C

B

A

Level 2 Geometry Final Exam 2010 Page 10

RS Q

P

30. (5 pts) Use the word bank to fill in the blanks for the two-column proof. Items in the word bank will

be used only once, and not all items will be used.

Prove: PQR PSR

Given:

PQPS

R is the midpoint of

SQ.

Statements Reasons

PQPS

Given

Definition of midpoint

PRPR

PQR PSR

Word Bank:

SPR QPR SSS Symmetric Property

SRQR

R is the midpoint of

SQ Reflexive Property Given S Q

Definition of bisector Isosceles Triangle

Theorem SAS HL

Level 2 Geometry Final Exam 2010 Page 11

31. (4 pts) Draw the resulting image after performing each transformation described below. Shade

your final image.

a) Reflect the triangle over the x-axis

b) Then, translate your new image by the rule (x, y) (x + 2, y – 3); (right 2, down 3)

32. (3 pts) Two ladders are leaning against a wall at

the same angle as shown creating similar

triangles.

How far up the wall does the shorter ladder

reach? Show all work.

14 ft

25 ft35 ft

x

y

h

Level 2 Geometry Final Exam 2010 Page 12

4 cm

P

N

M

33. (5 pts) Use the picture of MNP to figure out the missing parts. Show your work for each part.

Round your answers to the nearest tenth when necessary.

a. mN = ______________

b. mP = ______________

c. NP = _______________

34. (3 pts) Solve for x in the polygon below.

x = ____________________

35. ( 2 pts) Is it possible for a triangle to have sides with the given lengths of 16, 11, and 5? If not,

explain why.

Level 2 Geometry Final Exam 2010 Page 13

5 in

7 in

W

YX

40 °

60 °

Part IV. Explain What is Wrong

Directions: For each question, either explain what is wrong with the picture, statement, or formula

given, OR you can correct what is wrong with the picture, statement, or formula.

36.

37. M is the midpoint of

AB .

102-4

BMA

38.

AB is shown below:

AB

39. A student solves for side

YW by setting up the following equation:

72 52 WY 2

49 25 WY 2

74 WY 2

74 WY 2

8.6 WY

Level 2 Geometry Final Exam 2010 Page 14

40. What is wrong with the statement below?

A quadrilateral that has only one pair sides that are parallel and the other pair of sides that are

congruent must be a parallelogram. (Hint: try drawing a picture to help you)

41.

58° 70°

83°

140°

42. Given the quadrilateral ABCD and the measure of mA = 80, a student decides that mB = 95.

Area (6)2 36 43.

HAVE A GREAT SUMMER VACATION!

B C

DA

6 cm