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Name: ____________________________________ 6/13/2012

Circle your teacher: Mrs. Gordon Ms. McClellon Ms. Sheppard-Brick

Geometry Level 2 Final Exam 2012

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.

You are allowed to use your conjecture books on this exam.

The exam has 5 parts. Point values for each part appear below.

In total, there are 86 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. Fill in the blank

1 point each, 16 questions ___________ / 16

Part II. Multiple Choice

1 point each, 16 questions ___________ / 16

Part III. Short Answer

2-4 points each, 15 questions ___________ / 42

Part IV. Explain What is Wrong

2 points each, 3 questions ___________ / 6

Part V. Proof

6 points ___________ / 6

Total Points __________/ 86

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Part I

Directions: Fill-in-the-Blanks. Use the word bank provided for questions 1 - 15. Words may be used

more than once. (1 point each)

Use this word bank for the questions on the next page.

adjacent angle bisector vertex segment bisector

collinear complementary perpendicular consecutive

coplanar equilateral diagonal median

midsegment parallel parallelogram equiangular

supplementary prism trapezoid pyramid

reflection cylinder regular rotation

translation cone side skew

Use this word bank for the questions on the next page.

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Use the word bank from the previous page.

1. Two lines are ____________________ if they intersect to form a right angle.

2. The endpoint of the rays that form an angle is called its __________________.

3. A(n) _____________________ is a ray that divides an angle into two congruent angles.

4. Two angles are ____________________ if they have a common vertex and side, but no

common interior points.

5. Two lines are ____________________ if they lie in the same plane and do not intersect.

6. A(n) __________________ is a transformation that creates a mirror image.

7. A segment that connects two nonconsecutive vertices of a polygon is called a ___________.

8. A(n) ________________ is a quadrilateral with two pairs of opposite sides.

9. A regular polygon is _______________ and _______________.

10. The _______________ is a segment that connects the midpoints of two sides of a triangle.

11. _______________ 12. _______________ 13. ______________

14. ______________ 15. _______________ hexagon

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Part II Directions: Multiple Choice. Circle the letter of the best answer to the question. (1 point each)

1. Which of the following could represent the surface area of a sphere?

a. 9π cm

b. 9π cm2

c. 9π cm3

d. 9π cm4

2. What is the volume of the cone?

a. 3192 inp

b. 396 inp

c. 364 inp

d. 348 inp

3. Line m is a transversal. Which best describes Ð1 and Ð2?

a. alternate exterior angles

b. alternate interior angles

c. corresponding angles

d. vertical angles

4. A box of cereal is 18 inches by 3 inches by 12 inches. After breakfast, the box is one-third

full. How many cubic inches of cereal are left inside?

a. 36 in. 3

b. 72 in. 3

c. 216 in. 3

d. 648 in. 3

5. Lines l and m are parallel. Which statement is always true?

a. 2Ð and 4Ð are supplementary

b. 1Ð and 8Ð are supplementary

c. 1Ð and 3Ð are congruent

d. 6Ð and 7Ð are congruent

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6. Determine the transformation of ABCD to ''' CBAD

a. right 5 and up 1: (x + 5, y + 1)

b. left 5 and down 1: (x – 5, y – 1)

c. right 7 and up 4: (x + 7, y + 4)

d. left 7 and down 4: (x – 7, y – 4)

7. Which triangle classification is possible?

a. acute right

b. isosceles scalene

c. isosceles right

d. obtuse equiangular

8. Which congruence method would prove that these two triangles are congruent?

a. SSA

b. ASA

c. SAS

d. SSS

9. Given DCAB @ and DCAB // , which pair of congruence methods would prove that these

two triangles are congruent?

a. SSA or AAS

b. ASA or AAS

c. SAS or ASA

d. AAA or SSS

10. A jet is flying 7 miles above the ground. The pilot spots an airport as shown below.

What is the distance d from the plane to the airport?

a. 7 mi

b. 7 2 mi 9.9 mi

c. 7 3 mi 12.1 mi

d. 14 mi

d 7

mi

45

°

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11. In ABCD , BÐ is a right angle and o40=ÐAm . Which list shows the sides on order from

longest to shortest?

a. AB , BC, AC

b. BC , AB, AC

c. AC , BC, AB

d. AC , AB, BC

12. A triangle has two sides that have lengths of 7 cm and 17 cm. Which could represent the

length of the third side of the triangle?

a. 24 cm

b. 18 cm

c. 10 cm

d. 7 cm

13. Which statement below is true about an isosceles trapezoid?

a. Both pairs of opposite sides are parallel.

b. Both pairs of opposite sides are congruent.

c. One pair of opposite sides is congruent and the other is parallel.

d. One pair of opposite sides is both parallel and congruent.

14. Given the two triangles pictured below.

What measure for P would make ?

a. 35°

b. 55°

c. 90°

d. 145°

15. Which statement justifies that a. Exterior Angle

b. Linear Pair

c. Triangle Sum

d. Vertical Angle

16. What is the area of this parallelogram?

a. 240 cm2

b. 160 cm2

c. 96 cm2

d. 64 cm2

N

O P

J I

H

55°

12

10

20 cm

8 cm

cm

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Part III

2-4 points each

Directions: Answer the following questions. Full credit will be given for correct answers supported

with the appropriate work. Work that is partially correct may receive partial credit.

1. (3 points) Given the cylinder below with radius 4 cm and surface area p722cm , find the height.

2. (3 points) Given DNOB is similar to DLJH , solve for x.

3. (3 points) Solve for x.

4

x

x + 2

h = ______

x = ______

x = ______

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4. (3 points) In the diagram below, mÐABC = 42o . Solve for the value of x.

5. (3 points) In the diagram below, mÐFGH = 65o . What value of x would make line l parallel to

line m.

6. (3 points) Solve for the value of x in the quadrilateral below.

E

x = ______

a. mÐEGF = _____________

b. x = __________

x = ______

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7. (4 points) Given that quadrilateral TOAD @ quadrilateral FISH,

TO= 4x+12 ,

OA= 2x+17,

AD = 5x- 7, and

FI = 7x-6 . Solve for the value of x. (Hint: sketch FISH)

D

T O

A

8. (3 points) Draw and label a rectangle, a rhombus, and an isosceles triangle, each with a perimeter

of 36 units. Label all dimensions needed to find the perimeter, with appropriate numerical values.

Rectangle Rhombus Isosceles triangle

x = ______

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9. (3 points) A park manager is designing four different flower gardens. • Each garden will have a different shape. • Each garden will have an area of 64 square feet.

a. Draw a sketch of a garden that is shaped like a rectangle and has an area of 64

square feet. Be sure to label all the dimensions needed to determine the area. b. Draw a sketch of a garden that is shaped like a triangle and has an area of 64

square feet. Be sure to label all the dimensions needed to determine the area. c. Draw a sketch of a garden that is shaped like a trapezoid with bases of different

lengths and has an area of 64 square feet. Be sure to label all the dimensions needed to determine the area.

10. (2 points)

a. Identify two triangles are congruent by ASA _____ and _____

b. Identify two triangles are congruent by SAS _____ and _____

A CB

D E

84°

84° 84°

84°

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11. (2 points) In the diagram below, find the measure of ÐHOR and ÐSER .

ÐHOR =

ÐSER=

68

36

R

H

S E

O

12. (3 points) Using the diagram to the right, find a pair of angles that are:

a. vertical angles: ___________

b. congruent angles: ___________

c. supplementary angles: ___________

13. (2 points) Pat measures the length of the shadow of a tree

to be 54 feet long. At the same time he measures his

own shadow to be 12 feet long and his height to be 5

feet. How tall is the tree in feet?

54 ft

5 ft

12 ft

height = ______

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14. (3 points) Lulu needs to wallpaper four walls that are each 10 feet tall. A roll of wallpaper will

cover 60 square feet.

How many rolls of wallpaper should Lulu buy?

15. (2 points) Solve for x.

4x°

66°

88°

76°

90°

20 ft 15 ft

10 ft

Lulu should buy ______ rolls of wallpaper.

x = ______

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Part IV 2 points each

Directions: Circle the mistake and then either fix the mistake or explain what is wrong.

1. Find the area.

a. Circle the mistake in the following solution:

b1 = 40 b2 = 32 h =15

A =40 +32

2

æ

èç

ö

ø÷*15

A = 540

2. Given that rectangle PINK is similar to rectangle BLUE, find x.

10

x

5

8

a. Circle the mistake in the following solution:

5

10=

8

x

5x = 80

x =16

b. Fix the mistake or explain what is wrong

B L

U E

P I

N K

b. Fix the mistake or explain what is wrong

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3. Solve for x.

a. Circle the mistake in the following solution:

90 +138+3y = 360

3y =132

y = 44

x + 44 =180

x =136

b. Fix the mistake or explain what is wrong

x

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Part V 6 points

Directions: Fill in the missing statements and reasons in the proof below.

1. (3 points)

WXYV is a parallelogram

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2. Fix the 3 mistakes in the proof below. (3 points)

Given: QPu ruu

bisects ÐRQS , QR @QS

Prove: DRQP @ DSQP

Statement Reason

1. QR @QS 1. Reflexive Property

2. QPu ruu

bisects ÐRQS 2. Given

3. ÐRQP @ÐSQR 3. Definition of Bisects

4. QP @QP 4. Reflexive Property

5. DRQP @ DSQP 5. SSA