Geometry Level 2 Final Exam 2008 - SharpSchoolcamdencitywwhs.ss12.sharpschool.com/UserFiles/Servers/Server_344137/File/Migrate/About...Geometry Level 2 Final Exam 2008 Lexington High

Name: ____________________________________ 12 June 2008

Teacher (circle one) Buckus Haupt King Verner

Geometry Level 2 Final Exam 2008

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 formula sheet on the back of this cover sheet, which you may use at any point during the

exam.

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

In total, there are 115 points that you can earn. A letter grade scale will be set by the course faculty

after the tests have been graded.

Sections Points Earned (for teacher use only)

Part I. Fill-in the Blank

15 questions, 1 point each

___________ / 15

Part II. Short Answer

26 questions, 2 points each

___________ / 52

Part III. Long Answer

9 questions, 4 points each

___________ / 36

Part IV. Explain What is Wrong

6 questions, 2 points each

___________ / 12

Total Points Earned ___________ / 115

Exam Grade:__________________

Level 2 Geometry Final Exam 2008 Page 2

AB

Name: __________________________ Teacher: Buckus Haupt King Verner

Part I. Fill in the Blank

Directions: Use the word bank provided to complete each question. Words will be used

only once, and not all words will be used.

1. A triangle with no equal sides is called ________________________________.

2. A ray that splits an angle into to equal angles is called an angle _______________________.

3. _____________________________ lines intersect to form 90° angles.

4. A quadrilateral with 2 pairs of parallel sides is a(n) _____________________________.

5. An angle measuring 96° is classified as a(n) _________________________ angle.

6. The hypotenuse of a right triangles is always the ___________________________ side.

7. A quadrilateral with ONLY one pair of parallel sides is called a(n) __________________________.

8. If the sum of two angles is 180°, the angles are ________________________________.

9. Vertical angles are always _____________________________.

10. The diagonals of a ___________________________ intersect at 90° angles.

11. The diameter of a circle is equal to two times the _________________________.

12. Point A is the ________________________ of .

13. ________________ is the trigonometric ratio of the length of the leg opposite the angle to the

length of the hypotenuse.

14. The _________________________ of a triangle is perpendicular to its base.

15. The ________________________ of an isosceles triangle are equal in length.

acute complementary less parallelogram rhombus

altitude cosine line perpendicular right

angle diameter longest plane scalene

base endpoint median points shortest

bisector height midpoint radius sine

collinear isosceles obtuse rectangle supplementary

congruent legs parallel reflection trapezoid

Level 2 Geometry Final Exam 2008 Page 3

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: 24°, 3 in, 5 cm3, 12 ft

2)

Questions Answers

16. Find the measure of ∠A.

m∠A =_______________

17. Find the measure of ∠EHF.

m∠EHF = ____________

18. Name the shortest side of ΔIJK.

_________________

19. What is the intersection of plane RPQ and plane SMP?

Q

R

M

P

S

__________________

20. Find the coordinate of the midpoint of

!

RS .

7

R S

19

_____________

30°

20°

CA

B

35°

HD

EF

G

70°

60°50°KI

J

Level 2 Geometry Final Exam 2008 Page 4

C

A

X

W

Y B

Questions Answers

21. ∠1 and ∠2 are called: (pick one)

a. same-side interior angles

b. alternate interior angles

c. corresponding angles

d. alternate exterior angles __________________

22. Find the measure of ∠T.

m∠T = _______________

23. Complete the congruence statement ΔWXY ≅ Δ__________

ΔWXY ≅ Δ_____________

24. Calculate the missing side of the right triangle.

x = _________________

25. QUIZ is a parallelogram. Find the measure of ∠Q.

m∠Q = ______________

2

1

66°SR

T

8

6x

58°

Q U

IZ

Level 2 Geometry Final Exam 2008 Page 5

Questions Answers

26. Find the area of the circle. Give an exact answer or round your

decimal answer to the nearest tenth.

4 in

Area = _______________

27. Find the length of the midsegment of trapezoid TRAP.

MN = ______________

28.

!

AD, BE, and CF are medians of ΔACE.

If

!

AD =12 , find the measure of

!

AZ .

AZ = ______________

29. Which type of transformation is shown: reflection, rotation, or

translation?

__________________

30. Which type of transformation is shown: reflection, rotation, or

translation?

__________________

7 cm

13 cm

NM

T R

P A

Z

D

B

F

A

C

E

Level 2 Geometry Final Exam 2008 Page 6

Questions Answers

31. State the congruence postulate that you would use to show the

triangles are congruent (ex. SAS, SSS, etc.).

_____________

32. State the congruence postulate that you would use to show the

triangles are congruent (ex. SAS, SSS, etc.).

___________________

33. ABCD is similar to WXYZ. Find the measure of

!

YZ .

YZ = _________________

34. Calculate the surface area of the solid.

5

12

13

20

___________

35. Calculate the volume of the solid.

5

12

13

20

V = ________________

36. Evaulate the trig ratio. Write your answer as a decimal or a fraction.

cos A =

cos A = _______________

6

10.5

4

7

6

CB

A

D

YX

W

Z

3

5

4C

A

B

Level 2 Geometry Final Exam 2008 Page 7

Questions Answers

37. Calculate the area of the triangle.

6 m 2m

5 m

Area = ________________

38. Calculate the surface area of the cone. Give an exact answer or

round your decimal answer to the nearest tenth.

SA = __________________

39. Calculate the length of the missing leg using your knowledge of

special right triangles.

x = _____________

40. Calculate the area of rhombus ABCD.

!

AM = 3 ft

DM = 5 ft

Area = ______________

41. Calculate the length of the arc. Round your answer to the nearest

tenth.

Arc Length = ___________

x26

60°

30°

M

C D

B A

3 mm60°

6 cm

3 cm

Level 2 Geometry Final Exam 2008 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. Work that is partially correct

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

that use specific units.

42. Solve for x, then find the measure of ∠y.

x = ________________

y = ________________

43. The area of circle K is 78.5 inches.

a. Find the radius of circle K.

Radius = ________________

b. Use the radius you calculated to find the circumference of circle K. Round your answer to the

nearest tenth.

circumference = ________________

r

K

!

(3x + 4)°

!

(4 x "17)°

!

63°

!

y°

Level 2 Geometry Final Exam 2008 Page 9

44.

!

"ABC is equilateral. Solve for x and y.

x = __________________

y = __________________

45. DEFG is a rectangle.

a. Solve for x.

x = __________________

b. Use your answer from part a to calculate the length of one of the diagonals of rectangle DEFG.

Length of a diagonal = ________________

46. Each side of the cube has length x. Suppose the surface area of the cube is

!

150 cm2.

a. Solve for x. Round your answer to the nearest whole number.

x = __________________

b. Use your answer from part a to find the volume of the cube.

Volume = __________________

7y+4( )°

2x°

C

B

A

x

x

x

G

FE

D

5x-13

2x + 2

9

Level 2 Geometry Final Exam 2008 Page 10

47.

!

HK is parallel to

!

LN .

a. Solve for x.

x = __________________

b. Use your answer from part a to find the measure of ∠K.

m∠K = _________________

48. ΔPQR is a right triangle. Use trig ratios to answer part a.

Give all answers for this problem as decimals rounded to

the nearest tenth.

a. Solve for x

x = __________________

b. Solve for y.

y = __________________

b. Use your answers from parts a to find the perimeter of ΔPQR.

Perimeter = ___________________

93°

5x+17( )°

2x+23( )°

O

N

ML

K

J

IH

7 in!

24°

y

x QP

R

Level 2 Geometry Final Exam 2008 Page 11

49. Suppose, A = (-2, 1), B = (3, 1), and C = (3, -4). Plot the points and connect them to make a

triangle. Then find the area and perimeter of

!

"ABC .

Area = ________________

Perimeter = ________________

50. Quadrilateral STUV has the following angle measures:

!

"S =134o ,

!

"T = x # 4( )o

,

!

"U = x + 84( )o

,

and

!

"V = 46o . Note: No diagram is given for this question. You may wish to draw a diagram in the

space provided, but this is not required.

a. Solve for x.

x = __________________

b. Use your answer from part a to find the measure of each angle so that you can answer the

question: What type of quadrilateral is STUV? Be as specific as possible and explain your

answer.

Angle measurements:

Type of Quadrilateral:

Explanation:

4

2

-2

- 4

- 5 5

Level 2 Geometry Final Exam 2008 Page 12

100°

100°

80°

80°

Part IV. Explain What is Wrong

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

complete sentences. Your explanation may include what is wrong or how to fix the error.

51. Explain what is wrong with the solution:

Solve for w:

52. What is wrong with the picture?

53. Why can’t a triangle have the given side lengths?

4

16

11

!

2

7=

8

w " 4

8 # 7 = 2 w " 4( )

56 = 2w " 4

60 = 2w

30 = w

Level 2 Geometry Final Exam 2008 Page 13

54. A student decides that ΔABC ≅ ΔDEF by SAS. What is wrong with their reasoning?

55. A student claims that the triangle below can be classified as both an acute triangle and an obtuse

triangle because it has both acute and obtuse angles. What is wrong with this reasoning?

56. A student classifies the quadrilateral below as both a parallelogram and a trapezoid. Why is this not

possible?

25°120°

35°

D

E

F

CA

B