Geometry Midterm Exam Score: ______ / ______ Name: _____________________________ Student Number: ____________________ Answer the questions below. Make sure to show your work and provide complete geometric explanations for full credit. 1 Label the net for the figure below with its dimensions.   A. __________ B. __________ C. __________ 2 Name four rays shown. 3 You live in Carson City, Nevada, which has approximate (latitude, longitude) coordinates of (39N, 120W). Your friend lives in Ottawa, Ohio, with coordinates of (41N, 84W). You plan to meet halfway between the two cities. Find the coordinates of the halfway point. Show your work. 4 Write the conditional statement that the Venn diagram illustrates. 5 Is the following conditional true or false? If it is true, explain why. If it is false, give a counterexample. If it is snowing in Dallas, Texas, then it is snowing in the United States. 6 What is the value of x? Justify each step using proof reasoning. AB + BC = AC a.__________________________ 2x + 6x + 8 = 32 b. __________________________ 8x + 8 = 32 c. __________________________ 8x = 24 d. __________________________ X = 3 e. __________________________ 7 Give the missing reasons in this proof of the Alternate Interior Angles Theorem. Given: Prove: a. ________________________ b. ________________________ c. ________________________ 8  Based on the given information, can you conclude that ? Explain. Given: and , prove 9 Write the missing reasons to complete the proof. Given: , , and Prove: Statement Reason 1. 1. Given 2. 2. Given 3. 3. Given 4. 4. Definition of congruent segments 5. 5. ? 6. 6. Segment Addition Postulate 7. 7. Definition of congruent segments 8. 8. ? Step 5: _______________ Step 8: _______________ 10 Fill in the missing reasons to complete the proof. Given: , UY || TX Prove: Statement Reason 1. 1. Given 2. 2. Converse of the Corresponding Angles Postulate 3. 3. ? 4. 4. Given 5. 5. Transitive Property 6. 6. ? Step 3: ________________ Step 6: ________________ 11 Is  by HL? If so, name the legs that allow the use of HL. 12 Complete the proof by providing the missing reasons. Given: ,   Prove: Statement Reason 1. , , and 1. Given 2.  are right angles 2. Definition of perpendicular segments 3. 3.    ?   4. 4.    ?   5. 5.    ?   Step 3: ____________________ Step 4: ____________________ Step 5: ____________________ 13 Write a paragraph proof to show that . Given:  and 14 Given:  is the perpendicular bisector of IK. Name two lengths that are equal. 15 Li went for a mountain-bike ride in a relatively flat wooded area. She rode for 6 km in one direction and then turned and pedaled 16 km in another. Finally she turned in the direction of her starting point and r.

1. Geometry Midterm Exam
Score: ______ / ______
Name: _____________________________
Student Number: ____________________
Answer the questions below. Make sure to show your work and
provide complete geometric explanations for full credit.
1
Label the net for the figure below with its dimensions.
A. __________
B. __________

2. C. __________
2
Name four rays shown.
3
You live in Carson City, Nevada, which has approximate
(latitude, longitude) coordinates of (39N, 120W). Your friend
lives in Ottawa, Ohio, with coordinates of (41N, 84W). You
plan to meet halfway between the two cities. Find the
coordinates of the halfway point. Show your work.
4
Write the conditional statement that the Venn diagram
illustrates.
5
Is the following conditional true or false? If it is true, explain

3. why. If it is false, give a counterexample.
If it is snowing in Dallas, Texas, then it is snowing in the
United States.
6
What is the value of x? Justify each step using proof reasoning.
AB + BC = AC a.__________________________
2x + 6x + 8 = 32 b. __________________________
8x + 8 = 32 c. __________________________
8x = 24 d. __________________________
X = 3 e. __________________________

4. 7
Give the missing reasons in this proof of the Alternate Interior
Angles Theorem.
Given:
Prove:
a. ________________________
b. ________________________
c. ________________________
8
Based on the given information, can you conclude that ?
Explain.
Given: and , prove

5. 9
Write the missing reasons to complete the proof.
Given: , , and
Prove:
Statement
Reason
1.
1. Given
2.
2. Given
3.
3. Given
4.
4. Definition of congruent segments
5.
5. ?
6.
6. Segment Addition Postulate
7.
7. Definition of congruent segments
8.
8. ?
Step 5: _______________
Step 8: _______________

6. 10
Fill in the missing reasons to complete the proof.
Given: , UY || TX
Prove:
Statement
Reason
1.
1. Given
2.
2. Converse of the Corresponding Angles Postulate
3.
3. ?
4.
4. Given
5.
5. Transitive Property
6.
6. ?
Step 3: ________________
Step 6: ________________

7. 11
Is by HL? If so, name the legs that allow the use of HL.
12
Complete the proof by providing the missing reasons.
Given: ,
Prove:
Statement
Reason
1. , , and
1. Given
2. are right angles
2. Definition of perpendicular segments
3.
3. ?
4.
4. ?
5.
5. ?
Step 3: ____________________
Step 4: ____________________
Step 5: ____________________
13
Write a paragraph proof to show that .
Given: and

8. 14
Given: is the perpendicular bisector of IK. Name two lengths
that are equal.
15
Li went for a mountain-bike ride in a relatively flat wooded
area. She rode for 6 km in one direction and then turned and
pedaled 16 km in another. Finally she turned in the direction of
her starting point and rode 8 km. When she stopped, was it
possible that Li was back at her starting point? Explain.

9. 16
17
Judging by appearance, classify the figure in as many ways as
possible using rectangle, square, quadrilateral, parallelogram,
rhombus. Please justify your answers
18
For a regular n-gon:
a. What is the sum of the measures of its angles?
b. What is the measure of each angle?
c. What is the sum of the measures of its exterior angles, one at
each vertex?
d. What is the measure of each exterior angle?
e. Find the sum of your answers to parts b and d. Explain why

10. this sum makes sense.
a.
b.
c.
d.
e.

11. 19
Find the midpoint of each side of the trapezoid. Connect the
midpoints. What is the most precise classification of the
quadrilateral formed by connecting the midpoints of the sides of
the trapezoid?
20
Use the Distance Formula and the x-axis of the coordinate
plane. Show why the distance between two points on a number
line (the x-axis) is | a – b |, where a and b are the x-coordinates
of the points.
1

12. Name/Student Number: ________________________
Geometry Final Exam
Answer the questions below. Make sure to show your work and
provide complete geometric explanations for full credit.
1. A triangle has side lengths 10, 15, and 7. Is the triangle
acute, obtuse, or right? Show your work and explain.
2. A highway makes an angle of 6 with the horizontal. This
angle is maintained for a horizontal distance of 5 miles.
To the nearest hundredth of a mile, how high does the highway
rise in this 5-mile section? Show the steps you use to find the
distance.
3. A forest ranger spots a fire from a 28-foot tower. The angle
of depression from the tower to the fire is 11.

13. To the nearest foot, how far is the fire from the base of the
tower? Show the steps you use to find the solution.
4. State whether the transformation appears to be a rigid
motion. Explain.
5. How can you verify Euler’s formula for this net of a cube?
6. Jason designed an arch made of wrought iron for the top of a
mall entrance. The 11 segments between the two concentric
circles are each 1.25 m long. Find the total length of wrought
iron used to make the structure. Round the answer to the nearest
meter. Show your work.

14. 7. Consider the prism shown below.
Find the surface area of the prism. Show your work
8. Janine made a cylindrical vase in which the sum of the lateral
area and area of one base was about 3000 square centimeters.
The vase had a height of 50 centimeters. Find the radius of the
vase. Explain the method you would use to find the radius.
9. A design on the surface of a balloon is 5 cm wide when the

15. balloon holds 71 cm of air. How much air does the balloon hold
when the design is 10 cm wide? Explain the method you use to
find the amount of air.
10. In circle O, and are tangents. (The figure is not drawn to
scale.)
a.
Prove that .
b.
Find mBOD for mAOP = 64. Explain your reasoning.

16. 11. Determine whether a tangent line to circle O is shown in the
diagram, for AB = 7.75, OB = 4, and AO = 8.75. Explain your
reasoning. (The figure is not drawn to scale.)
12. In circle O, CD = 44, OM = 20, ON = 19, , (The figure is
not drawn to scale.) Show your work.
a.
Find the radius. If your answer is not an integer, express it in
radical form.
b.
Find FN. If your answer is not an integer, express it in radical
form.
c.
Find EF. Express it as a decimal rounded to the nearest tenth.
13.
is tangent to the circle at B. mA = 14 and (The figure is not
drawn to scale.) Show your work.

17. a.
Find x.
b.
Find y.
14. At a track meet, 50 people ran the 100-meter dash. 2 people
finished in 11 seconds, 5 people finished in 12 seconds, 8
people finished in 13 seconds, 10 people finished in 14 seconds,
21 people finished in 15 seconds, 2 people finished in 16
seconds, and 2 people finished in 17 seconds. What is the
probability distribution for the finish times?
15. Is there a similarity transformation that maps to ? If so,
identify the similarity transformation and write a similarity

18. statement. Explain your answer.
16. Janine wants to paint just the sides of a cylindrical pottery
vase that has a height of 45 cm and a diameter of 14 cm. To the
nearest whole number, find the number of square centimeters
she will need to paint. Explain the method you would use to
find the lateral area.
17. Determine whether a tangent line is shown in the diagram,
for AB = 7, OB = 3.75, and AO = 8. Explain your reasoning.
(The figure is not drawn to scale.)
18. The equation (x + 5) + (y + 3) = 169 models the position
and range of the source of a radio signal. Describe the position
of the source and the range of the signals.

19. 19. An hourglass, composed of two identical cones, is 12 cm
tall. The radius of each cone is 3 cm. If you want to fill the
bottom half of the hourglass full of salt, how much salt will
you need? Explain the method you would use to find the amount
of salt.
20. Three balls are packaged in a cylindrical container as shown
below. The balls just touch the top, bottom, and sides of the
cylinder. The diameter of each ball is 13 cm.
a. What is the volume of the cylinder? Explain your method
for finding the volume.
b. What is the total volume of the three balls? Explain your

20. method for finding the total volume.
c. What percent of the volume of the container is occupied by
the three balls? Explain how you would find the percent.
CB

21. AD
FE
3
44
6
88