Geometry
Final Review
2014
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
1. Q is equidistant from the sides of
Find
The diagram is not to scale. (Ch5)
(Hint: RS is an angle bisector)
T
|
(2
x
|
+
5)
°
Q
(5x – 25)°
S
R
____
a. 25
b. 10
c. 20
2. What is the name of the segment inside the large triangle?
____
(Look up definitions for each of the choices)
a. perpendicular bisector
c. median
b. altitude
d. midsegment
3. Find the values of the variables and the lengths of the sides of this kite. (Ch6)
y–2
|
d. 50
(Ch5)
x+ 2
||
||
|
2x + 2
x + 11
(Look up definition of a Kite)
a. x = 9, y = 13; 7, 15
b. x =13, y = 9; 7, 15
c. x = 9, y = 13; 11, 20
d. x =13, y = 9; 11, 11
____
4. What is the most precise name for quadrilateral ABCD with vertices A(–5, 2), B(–3, 6), C(6, 6), and D(4, 2)?
a. quadrilateral
b. rectangle
c. parallelogram
d. rhombus
(Use slope formula to eliminate a rectangle & the distance formula to iliminate the rhombus) – Ch6
____ 5. ABCD is a parallelogram. If
then
The diagram is not to scale. (Ch6)
A
D
a. 66
B
C
(What do you know about adjacent angles on a parallelogram?)
b. 124
c. 114
d. 132
1
____
6. Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale. (Ch6)
M
N
A
P
O
(What do you know about the diagonals of a parallelogram?)
b. 4
c. 9
d. 4.5
a. 8
Find the area. The figure is not drawn to scale.
____
7.
(What is the formula for the area of a parallelogram?) (Ch11)
7.6 cm
3.7 cm
a.
b.
c.
d.
____
8. A grid shows the positions of a subway stop and your house. The subway stop is located at (–5, 2) and your
house is located at (–9, 9). What is the distance, to the nearest unit, between your house and the subway stop?
(Use the distance formula, since you are given 2 points) Ch6
a. 5
b. 13
c. 8
d. 18
____ 9. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain. (Ch7)
(Use the converse of the pythagorean theorem – look it up)
a. yes;
c. no;
b. no;
d. yes;
____ 10. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
(Use Trigonometry, or special triangles) – Ch7
16
45°
Not drawn to scale
a. 128
b.
8 2
c. 16
d.
2 2
2
Find the area of the trapezoid. Leave your answer in simplest radical form.
____ 11. Find the area of the rhombus. (Ch11) (Look up the formula for a rhombus.)
8m
8m
8m
8m
a. 12 m2
b. 4096 m2
c. 128 m2
d. 32 m2
____ 12. Find the area of the regular polygon. Round your answer to the nearest tenth. (Ch11)
13.07 in.
10 in.
a. 176.6 in.2
(See your presentation notes, or see ch11.3)
b. 966.1 in.2
c. 80.0 in.2
d. 483.0 in.2
____ 13. Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The
results are shown in the circle graph below. Find the measure of each central angle in the circle graph. (Ch10)
a. Sleeping
(Use the fact that there are 360 degrees around the circle and multiply by the part)
b. Eating
a. 118.8°; 28.8°
b. 108°; 28.8°
c. 118.8°; 288°
d. 59.4°; 288°
3
____ 14. Identify a semicircle that contains C. (Ch10)
C
A
B
0
(Look up 10.1 for how to name a semicircle, minor, major arcs)
a. semicircle ABC
c. semicircle CB
b. semicircle AC
d. semicircle ACB
Find the circumference. Leave your answer in terms of .
(Ch10, Ch11) (Look up formula for how to find the circumference of a circle.)
____ 15.
18 in.
a.
in.
b.
in.
c.
in.
d.
in.
____ 17. The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the
height of the model to the height of the actual Sears Tower? (Ch7)
(Look up in ch7, how to find ratios and scale factors)
a. 1 : 725
b. 725 : 1
c. 12 : 725
d. 725 : 12
Solve the proportion. (Ch7.1)
(Look up ratios and proportions)
____ 18.
a.
1
b. 5
c.
1
d. 25
25
____ 19. On a blueprint, the scale indicates that 6 cm represent 15 feet. What is the length of a room that is 9 cm long
and 4 cm wide on the blueprint? (Ch7) (Look up proportions)
a. 22.5 ft
b. 1.5 ft
c. 6 ft
d. 16.5 ft
4
____ 20.
. Complete the statements. (Ch7-2, look up similar polygons)
A
G
E
B
F
H
D
J
C
a.
b.
GH

AB
DJ
a.
b. E; AE
; DC
c. E; DC
d.
; AE
____ 21. Are the triangles similar? If so, explain why. (Ch7-3, look up postulate and theorems about similar
triangles)
30.4°
84.6°
84.6°
a. yes, by SAS
65°
b. yes, by SSS
c. yes, by AA
d. No
____ 22. Use the information in the diagram to determine the height of the tree to the nearest foot.
a. 80 ft
b. 264 ft
(Ch7-1, look up proportions)
c. 60 ft
d. 72 ft
____ 23. Find the geometric mean of 5 and 6. (Ch8-1, look up def. of geometric mean)
a. 30
b.
6
c.
35
d.
30
5
The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to
the second. The figures are not drawn to scale. (Any side of a triangle is proportional to its perimeter, and
to the square of its area).
____ 24.
15
18
a. 5 : 6 and 25 : 36
b. 6 : 7 and 36 : 49
c. 5 : 6 and 36 : 49
d. 6 : 7 and 25 : 36
____ 25. Write the tangent ratios for
and
. (Review the 3 trig. Rations Ch8-4)
Z
85
7
X
Y
6
Not drawn to scale
a.
c.
b.
d.
Find the value of x. Round your answer to the nearest tenth. (Ch8-3, review special triangles)
____ 26.
7

x
Not drawn to scale
a. 3.5
b. 12.1
____ 27.
c. 6.1
d. 4
(Review the 3 trig. Rations Ch8-4)
x

9
Not drawn to scale
6
a. 3.3
b. 3.1
c. 24.7
Find the value of x to the nearest degree.
____ 28.
(Ch8-4, Review the 3 trig. inverses)
d. 8.5
58
3
x
a. 67
____ 29.
b. 22
c. 83
d. 53
Find the value of x. Round to the nearest tenth.
(Review the 3 trig. Rations Ch8-4)
x
18

Not drawn to scale
a. 10.3
b. 31.4
c. 10.7
d. 31.8
____ 30. Viola drives 170 meters up a hill that makes an angle of 6 with the horizontal. To the nearest tenth of a
meter, what horizontal distance has she covered? (Ch8-5, review angles of elevation and depression)
a. 171.5 m
b. 169.1 m
c. 1617.4 m
d. 17.8 m
Find the value of x. Round the length to the nearest tenth.
____ 31.
(Ch8-5, review angles of elevation and depression)

x
200 m
Not drawn to scale
a. 1134.3 m
b. 1151.8 m
c. 34.7 m
d. 203.1 m
Find the area of the regular polygon. Give the answer to the nearest tenth.
____ 32. hexagon with side 8 yd (Ch11-3, review how to find the area of a polygon inscribed in a circle)
a. 332.6 yd
b. 12 yd
c. 41.6 yd
d. 166.3 yd
____ 33. square with radius 16 ft
7
a. 520 ft
b. 512 ft
c. 256 ft
d. 1024 ft
Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale.
____ 34.
(Ch8, Ch11, Use trig. To find the height and use formula for the area of a triangle)
4.7 m

6.1 m
a. 10.5 m
b. 9.8 m
c. 19.6 m
d. 21.0 m
Use formulas to find the lateral area and surface area of the given prism. Show your answer to the
nearest whole number.
____ 35.
(Ch12, look up how to find the volume of a triangular prism)
6
36
3
5
Not drawn to scale
a. 468 m ; 519 m
b. 468 m ; 534 m
c. 504 m ; 512 m
d. 504 m ; 519 m
Find the surface area of the cylinder in terms of .
____ 36.
(Ch12, look up how to find the volume of a cylinder)
14 cm
15 cm
Not drawn to scale
a. 518 cm
b. 602 cm
c. 812 cm
d. 308 cm
8
____ 37.
Find the volume of the given prism. Round to the nearest tenth if necessary.
(Ch12, look up how to find the area of a box, or rectangular prism)
4 ft
7 ft
11 ft
Not drawn to scale
a. 308 ft
b. 301 ft
c. 298 ft
d. 312 ft
Find the volume of the square pyramid shown. Round to the nearest tenth as necessary.
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of
x. (Figures are not drawn to scale.)
____ 38.
12
(Ch10, look up the meaning of a tangent line and its relationship to a radius to the point of
tangency)
Q
P
x°
O
a. 78
____ 39.
b. 39
c. 102
d. 24
is tangent to circle A at B and to circle D at C (not drawn to scale).
AB = 7, BC = 18, and DC = 5. Find AD to the nearest tenth. (Ch10, look up the meaning of a tangent line
and its relationship to a radius to the point of tangency)
B
C
A
D
a. 18.7
b. 18.1
c. 21.6
d. 19.3
_____ 40. Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not
drawn to scale.
(Ch10, look up the relationship between a chord and radius ^ to it.)
6
8
x
a. 8
b. 5
c. 6
d. 10
9
____ 41. The radius of circle O is 18, and OC = 13. Find AB. Round to the nearest tenth, if necessary. (The figure is not
drawn to scale.)
C
A
B
O
(Ch10, look up the relationship between a chord and radius ^ to it.)
a. 12.4
b. 3.8
c. 24.9
d. 44.4
____ 42. Find the measure of BAC. (The figure is not drawn to scale.) (Ch10, look up inscribed vs central angles)
A
O

C
B
a. 57
b. 28.5
c. 33
d. 114
____ 43. The dashed triangle is a dilation image of the solid triangle. What is the scale factor? (Ch7-6, look up
similarity transformations)
y
8
4
–8
–4
4
8
x
–4
–8
a.
b.
c.
d. 2
The answers to the problems above begin on the next page.
10
Geometry
Final Exam
Answer Section
2014
MULTIPLE CHOICE
1. ANS: D
DIF: L2
REF: 5-2 Bisectors in Triangles
OBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors
TOP: 5-2 Example 2
KEY: Converse of the Angle Bisector Theorem,angle bisector
2. ANS:
OBJ:
TOP:
KEY:
D
DIF: L1
REF: 5-3 Concurrent Lines¸ Medians¸ and Altitudes
5-3.2 Medians and Altitudes
5-3 Example 4
altitude of a triangle,angle bisector,perpendicular bisector,midsegment,median of a triangle
3. ANS: C
DIF: L1
REF: 6-1 Classifying Quadrilaterals
OBJ: 6-1.1 Classifying Special Quadrilaterals
TOP: 6-1 Example 3
KEY: algebra,kite
4. ANS: C
DIF: L1
REF: 6-1 Classifying Quadrilaterals
OBJ: 6-1.1 Classifying Special Quadrilaterals
TOP:
6-1 Example 2
KEY: kite,parallelogram,quadrilateral,special quadrilaterals,rectangle,square,trapezoid
5. ANS: C
DIF: L1
OBJ: 6-2.1 Properties: Sides and Angles
TOP: 6-2 Example 1
REF: 6-2 Properties of Parallelograms
KEY: parallelogram,consectutive angles
6. ANS: B
DIF: L1
REF: 6-2 Properties of Parallelograms
OBJ: 6-2.2 Properties: Diagonals and Transversals
KEY: parallelogram,diagonal,Theorem 6-3
7. ANS: A
DIF: L1
OBJ: 7-1.1 Area of a Parallelogram
TOP: 7-1 Example 1
8. ANS:
OBJ:
TOP:
KEY:
REF: 7-1 Areas of Parallelograms and Triangles
KEY: area,parallelogram,base,height
C
DIF: L2
REF: 7-2 The Pythagorean Theorem and Its Converse
7-2.1 The Pythagorean Theorem
7-2 Example 3
Pythagorean Theorem,leg,hypotenuse,word problem,problem solving
9. ANS: C
DIF: L1
REF: 7-2 The Pythagorean Theorem and Its Converse
OBJ: 7-2.2 The Converse of the Pythagorean Theorem
TOP: 7-2 Example 5
KEY: Pythagorean Theorem
10. ANS: B
DIF: L1
OBJ: 7-3.1 45°-45°-90° Triangles
TOP: 7-3 Example 2
REF: 7-3 Special Right Triangles
11. ANS: C
REF: 7-4 Areas of Trapezoids¸ Rhombuses¸ and Kites
DIF: L1
KEY: special right triangles,hypotenuse,leg
11
OBJ: 7-4.2 Finding Areas of Rhombuses and Kites
TOP: 7-4 Example 4
KEY: area,rhombus
12. ANS: D
DIF: L1
REF: 7-5 Areas of Regular Polygons
OBJ: 7-5.1 Areas of Regular Polygons
TOP: 7-5 Example 3
KEY: regular
polygon,area,apothem,radius,octagon
13. ANS: A
DIF: L1
REF: 7-6 Circles and Arcs
OBJ: 7-6.1 Central Angles and Arcs
TOP: 7-6 Example 1
KEY: central angle,circle graph,multi-part question,word problem,problem solving
14. ANS: D
DIF: L1
OBJ: 7-6.1 Central Angles and Arcs
TOP: 7-6 Example 2
REF: 7-6 Circles and Arcs
KEY: major arc,minor arc,semicircle
15. ANS: B
DIF: L1
REF: 7-6 Circles and Arcs
OBJ: 7-6.2 Circumference and Arc Length
TOP:
7-6 Example 4
KEY: circumference,radius
16. ANS:
OBJ:
TOP:
KEY:
D
DIF: L1
REF: 7-8 Geometric Probability
7-8.1 Using Segment and Area Models
7-8 Example 2
geometric probability,segment,word problem,problem solving
17. ANS: A
DIF: L1
REF: 8-1 Ratios and Proportions
OBJ: 8-1.1 Using Ratios and Proportions
TOP:
8-1 Example 1
KEY: ratio,word problem
18. ANS: D
DIF: L1
REF: 8-1 Ratios and Proportions
OBJ: 8-1.1 Using Ratios and Proportions TOP: 8-1 Example 3
KEY: proportion,Cross-Product Property
19. ANS: A
DIF: L1
REF: 8-1 Ratios and Proportions
OBJ: 8-1.1 Using Ratios and Proportions
TOP:
8-1 Example 4
KEY: proportion,Cross-Product Property,word problem
20. ANS: A
DIF: L1
OBJ: 8-2.1 Similar Polygons TOP:
21. ANS:
OBJ:
TOP:
KEY:
REF: 8-2 Similar Polygons
8-2 Example 1
KEY: similar polygons
C
DIF: L1
REF: 8-3 Proving Triangles Similar
8-3.1 The AA Postulate and the SAS and SSS Theorems
8-3 Example 2
A-A Similarity Postulate, SSS & SAS Similarity Theorems
22. ANS: A
DIF: L1
REF: 8-3 Proving Triangles Similar
OBJ: 8-3.2 Applying AA¸ SAS¸ and SSS Similarity
TOP: 8-3 Example 4
KEY: Angle-Angle Similarity Postulate,word problem
23. ANS: D
DIF: L2
REF: 8-4 Similarity in Right Triangles
OBJ: 8-4.1 Using Similarity in Right Triangles TOP:8-4 Example 1 KEY: geometric mean,proportion
12
24.
ANS: A
DIF: L2
REF:8-6 Perimeters and Areas of Similar Figures
OBJ: 8-6.1 Finding Perimeters and Areas of Similar Figures
TOP: 8-6 Example 1
KEY: perimeter,area,similar figures
25. ANS: C
DIF: L2
REF: 9-1 The Tangent Ratio
TOP: 9-1 Example 1
KEY: leg adjacent to angle,leg opposite angle,tangent,tangent ratio
26. ANS: D
DIF: L1
OBJ: 9-1.1 Using Tangents in Triangles
TOP: 9-1 Example 2
REF: 9-1 The Tangent Ratio
27. ANS: C
DIF: L1
OBJ: 9-1.1 Using Tangents in Triangles
TOP: 9-1 Example 2
REF: 9-1 The Tangent Ratio
28. ANS:
OBJ:
TOP:
KEY:
KEY: side length using tangent,tangent,tangent ratio
KEY: side length using tangent,tangent,tangent ratio
B
DIF: L2
REF: 9-1 The Tangent Ratio
9-1.1 Using Tangents in Triangles
9-1 Example 3
inverse of tangent,tangent,tangent ratio,angle measure using tangent
29. ANS: B
DIF: L1
REF: 9-2 Sine and Cosine Ratios
OBJ: 9-2.1 Using Sine and Cosine in Triangles
TOP: 9-2 Example 2
KEY: sine,side length using since and cosine,sine ratio
30. ANS:
OBJ:
TOP:
KEY:
B
DIF: L2
REF: 9-2 Sine and Cosine Ratios
9-2.1 Using Sine and Cosine in Triangles
9-2 Example 2
cosine,word problem,side length using since and cosine,problem solving,cosine ratio
31. ANS:
OBJ:
TOP:
KEY:
B
DIF: L1
REF: 9-3 Angles of Elevation and Depression
9-3.1 Using Angles of Elevation and Depression
9-3 Example 3
sine,side length using since and cosine,sine ratio,angles of elevation and depression
33. ANS: D
DIF: L1
REF: 9-5 Trigonometry and Area
OBJ: 9-5.1 Finding the Area of a Regular Polygon
TOP: 9-5 Example 1
KEY: area of a regular polygon,area,regular polygon,tangent,measure of central angle of a regular polygon
34. ANS: B
DIF: L1
REF: 9-5 Trigonometry and Area
OBJ: 9-5.1 Finding the Area of a Regular Polygon
TOP: 9-1 Example 2
KEY: area of a regular polygon,area,regular polygon,cosine,sine,measure of central angle of a regular
polygon
35. ANS:
OBJ:
KEY:
36. ANS:
OBJ:
KEY:
A
DIF: L1
REF: 9-5 Trigonometry and Area
9-5.2 Finding the Area of a Triangle
TOP:
9-5 Example 3
area of a triangle,area,sine
D
DIF: L1
REF: 10-3 Surface Areas of Prisms and Cylinders
10-3.1 Finding Surface Area of a Prism
TOP:
10-3 Example 2
surface area formulas,lateral area,surface area,prism,surface area of a prism
13
37. ANS: D
DIF: L1
REF: 10-3 Surface Areas of Prisms and Cylinders
OBJ: 10-3.2 Finding Surface Area of a Cylinder TOP:
10-3 Example 3
KEY: surface area of a cylinder,cylinder,surface area formulas,surface area
38. ANS: A
DIF: L1
REF: 10-4 Surface Areas of Pyramids and Cones
OBJ: 10-4.2 Finding Surface Area of a Cone TOP:
10-4 Example 3
KEY: surface area of a cone,surface area formulas,surface area,cone
39. ANS:
OBJ:
KEY:
40. ANS:
OBJ:
KEY:
A
DIF: L1
REF: 10-5 Volumes of Prisms and Cylinders
10-5.1 Finding Volume of a Prism TOP: 10-5 Example 1
volume of a rectangular prism,volume formulas,volume,prism
B
DIF: L1
REF: 10-6 Volumes of Pyramids and Cones
10-6.1 Finding Volume of a Pyramid
TOP:
10-6 Example 1
volume of a pyramid,pyramid,volume formulas,volume
41. ANS: A
DIF: L1
REF: 11-1 Tangent Lines
OBJ: 11-1.1 Using the Radius-Tangent Relationship
TOP: 11-1 Example 1
KEY: tangent to a circle,point of tangency,angle measure,properties of tangents,central angle
42. ANS: B
DIF: L1
REF: 11-1 Tangent Lines
OBJ: 11-1.1 Using the Radius-Tangent Relationship
TOP: 11-1 Example 2
KEY: tangent to a circle,point of tangency,properties of tangents,Pythagorean Theorem
43. ANS:
OBJ:
TOP:
KEY:
D
DIF: L1
REF: 11-2 Chords and Arcs
11-2.2 Lines Through the Center of a Circle
11-2 Example 3
bisected chords,circle,perpendicular,perpendicular bisector,Pythagorean Theorem
44. ANS: B
DIF: L1
OBJ: 11-4.2 Finding Segment Lengths
TOP: 11-4 Example 3
45. ANS:
OBJ:
TOP:
KEY:
REF: 11-4 Angle Measures and Segment Lengths
KEY: circle,intersection outside the circle,secant
C
DIF: L1
REF: 11-2 Chords and Arcs
11-2.2 Lines Through the Center of a Circle
11-2 Example 3
bisected chords,circle,perpendicular,perpendicular bisector,Pythagorean Theorem
46. ANS: B
DIF: L2
REF: 11-3 Inscribed Angles
OBJ: 11-3.1 Finding the Measure of an Inscribed Angle
TOP: 11-3 Example 2
KEY: circle,inscribed angle,intercepted arc,inscribed angle-arc relationship
48. ANS: B
DIF: L1
OBJ: 12-7.1 Locating dilation images
TOP: 12-7 Example 1
REF: 12-7 Dilations
KEY: dilation,reduction,scale factor
14