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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