Geometry
Semester 2
Final Review ANSWERS 
NAME:KRUZY’S KEY
DATE:
PERIOD:
You will need to show your work on another piece of paper as there is simply not enough room on
this worksheet. This is due in completion on the day of your assigned final exam time. 20 points.
1.
Identifying Types of Symmetry:
A
a.
b.
c.
d.
2.
(all boxes are squares)
C
B
Which pictures shown above demonstrate reflectional symmetry?
A and B
Which pictures have rotational symmetry?
B and C
Which pictures have translational symmetry?
A and B and C
Show or describe the symmetry for each part a-c.
A has vertical line down the center
B has vertical line and horizontal lines down centers and 180 degree rotation
C has 180 rotational symmetry
They can all slide to produce original picture
Writing Ordered Pair Rules:
a. Write an ordered pair rule
(x, y)(x+5, y-3)
b. Write an ordered pair rule
(x, y)(x-1, y+4)
c. Write an ordered pair rule
(x, y)(x, -y)
d. Write an ordered pair rule
(x, y)(-x, y)
e. Write an ordered pair rule
for a translation 3 units down and 5 units right.
for a translation 1 unit left and 4 units up.
for a reflection over the x-axis.
for a reflection over the y-axis.
for a reflection over the line y  x .
(x, y)(y, x)
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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3.
Find the missing sides in these 30  60  90 triangles:
e
3cm
30
b
a
c
30
15cm
8cm
f
h
g
30
9 3 cm
30
d
a = 6 cm
b = 3 3 cm
4.
c = 4 3 cm
d = 4 cm
e = 5 3 cm
f = 10 3 cm
g = 9 cm
h = 18 cm
Find the missing sides in these isosceles right triangles:
w
v
u
4 2 cm
x
z
y
6cm
5cm
u = 5 cm
v = 5 2 cm
5.
w = 4 cm
x = 4 cm
y = 3 2 cm
z = 3 2 cm
Proof Vocabulary: Describe the difference between a postulate and a theorem.
A postulate is assumed true within the mathematical community.
A theorem is proven using deductive reasoning.
6.
Fill in the missing step of the following proof.
This problem checks on your understanding of algebra and the official POE names.
Remember POE, Properties of Equality?
Given: 3x  15  14x  2
Prove: x  1
Statement
1. 3x  15  14x  2
2. 15  17x  2
3. ? 17  17 x
4. 1  x
5. x  1
Reason
1. Given
2. Addition Property of Equality
3. ?Subtraction POE
4. Multiplication Property of Equality
5. Symmetric Property of Equality
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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7.
Andrena watched a bug crawl along an arc of 12 along the rim of her bike wheel. If the
radius of the wheel was 3 inches, how far did the bug crawl?
This is asking you to find the length of the arc.
12
1

A.L.  %of circle x circumference 
 (2  3)   (6 )  in  0.6283 in
360
30
5
8.
Trigonometry: Find x in the following right triangles.
a.
b.
32
c.
18in
x
5 in
26
x
7 in
x
15in
x = 35.54
x = 28.31
x = 16.18
d. A guy wire is anchored 8 meters from the base of a pole. The wire makes a 62 degree
angle with the ground. How long is the wire? 17.040 m
9.
Distance Formula: Find the perimeter of ABC with vertices A(3, 4) , B(2,5) and C (6, 2) .
Perimeter = 22.437 and it’s scalene
10.
Area Formulas: Find the areas of the following...
a.
b. Area = 160 sq in
c.
26
24
10in
14ft
24
8in
25
7
25
Find Perimeter.
60
area = 24.5 3
d.
26
10
perimeter = 60 in
Regular Hexagon
e.
apothem = 4.6 in
side lengths = 5.9 in
30
f. Circle whose
circumference
= 12 in
area = 408
g.
20in
8in
24in
area = 81.42
shaded area & r=6in
area = 33
area = 36
area = 176
h. Find the area of an equilateral triangle with one side that is 8 inches. 16 3
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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i. A circle is inscribed inside a square. The square measures 12 cm per side. Find the area
outside the circle but inside the square. 30.903
11.
Surface Area: Find the SA or the indicated parts for the following.
a. Sphere
b. Cylinder
c. Square Based Pyramid
radius = 11 in
radius = 5 in
base sides = 5in
height = 8 in
slant height = 16in
SA = 484
SA = 130
SA = 185
d.
Cone
diameter = 10 in
slant height = 16 in
e. Rectangular Prism
SA = 340 sq in
height = 5 in
length = 10 in
Find width.
w=8
SA = 105
12.
f. Sphere SA = 576
Find Radius.
r = 12 in
Volume Formulas: Find the Volume or the indicated parts for the following.
a. Sphere
b. Half of a Cylinder
c. Square Based Pyramid
radius = 11 in
radius = 5 in
base sides = 5in
height = 8 in
 height = 14in
5324
350
V=
V = 100
V=

 116.667
3
3
d.
Cone Vol = 720in
 height = 14 in
Find Radius.
Find Diameter.
e. Triangular Prism
at the right...
V = 280
5in
3
r  7.0079in
d  14.0158in
f.
14in
8in
Trapezoidal Based Pyramid
V = 525
g. Hemisphere
radius = 9 cm
V  486 cm3
13.
Pythagorean Theorem:
a. Find x.
b. Find x.
x
7
x=
113
8
18
x
x=
15
99
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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c.
Is this a right triangle?
d. Is this a right triangle?
25
19
50
14
20
48
No b/c 192  202  761 but 252  625
yes b/c 142  482  2500  502
e.
f. Find the length of the diagonal in the box from
the front upper left corner to the back lower
right corner.
Find x.
x+18
24
x=7
Diagonal = 14.317
6
x
5
14.
Similarity Ratios and Calculating Area:
Two triangles are similar and have side ratios 2:3.
a. Find the ratio of their heights. 2:3
b. Find the ratio of their medians. 2:3
c. Find the ratio of their perimeters. 2:3
d. Find the ratio of their areas. 4:9
e. If the area of the larger triangle is 50in2 , then find the area of the smaller triangle.
Smaller area = 22.222
15.
Similarity Ratios and Calculating Volume:
Two cylinders are similar and have a volume ratio of 8:343
a. What is the ratio of their radii? 2:7
b. What is the ratio of their diameters? 2:7
c. What is the ratio of their heights? 2:7
d. What is the ratio of their surface areas? 4:49
e. If the volume of the smaller cylinder is 100cm3 , the find the volume of the larger
cylinder. Volume larger = 4287.5
12
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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16.
Similarity Conjectures:
a. Name the three triangle similarity conjectures.
AA Similarity
SSS Similarity
b. Draw a picture of each.
SAS Similarity
D
D
D'
CD = 6.10 cm
CD' = 3.05 cm
C'
C
17.
DA = 6.00 cm
DA' = 3.00 cm
D'
CD = 6.10 cm
CD' = 3.05 cm
A'
AC = 4.42 cm
AC' = 2.21 cm
A
42ft
c. Find the requested measurements.
All units are in centimeters.
HAPIE~FORTH
H
6
A
P
7
19.2
4
I
E
O
32
R
F
H
28.8
A'
C'
A
C
Writing and Solving Proportions from Figures:
a. Find x.
b. Find x and y.
X = 12
x = 10 and y = 12 7ft
5x+3
x
3.5ft
8ft
DA = 6.00 cm
DA' = 3.00 cm
x
8ft
5ft
y
d. If a 16 m street light casts a 15 m
shadow at the same time a person casts
a 4 m shadow, how tall is the person?
4.266m
AP  10
EI  9
FH  22.4
RT  12.8
T
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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18.
Equations of Circles:
a. Write the equation of a circle if the radius is 5 and the center is at (0, 4).
x 2  (y  4)2  25
b. Write the equation of a circle if the radius is 6 and the center is at (-1, -2).
(x  1)2  (y  2)2  36
c. If (x  5)2  (y  3)2  49 , then find the radius and the center.
Radius = 7 Center = (5, -3)
d. If x  (y  9)2  1 , then find the radius and the center.
2
Radius = 1 Center = (0, 9)
The radius is 15 mm.
Find the length of arc QD.
There are for sure TWO arc length problems on the final!!
Remember that arc measure uses degrees,
but, arc length uses lengths like inches or millimeters.
80
2
20
A.L.  %of circle x circumference 
 (2 15)   (30 )   mm
360
9
3
Q
19.
20.
D
O
40
E
Proving Triangles Congruent:
A
a. GIVEN: Isosceles ABC
AD is the altitude of ABC
PROVE: ABD  ACD
B
D
C
ABC is an
isosceles
AB  AC
Given
Definition of
Isosceles
AD is the altitude
of ABC
ADB = 90°
ADC = 90°
ADB  ADC
Given
Definition
of Altitude
Transitive POE
ADB 
ADC
HL
AD  AD
Reflexive
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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A
b.
A
GIVEN: AB || DE
A
D
C is the midpoint of AE
PROVE: ABC  EDC
D
C
B
C
B
AAS
C
B
AAS
E
3 different solutions possible
D
E
ASA
E
CAB  CED or
ABC  EDC
AB || DE
Given
AIA
C is the midpoint
of AE
ACB 
EC  AC
Definition of
Midpoint
Given
ECD
AAS or ASA
ACB  ECD
Vertical Angle
Conjecture
21.
Finding Arc Length:
a. Find the arc length of SR
if the radius is 11 cm.
77
 cm  13.4390cm
18
b. Find the arc length of AC
if the radius is 17 m.
34
 cm  11.8682cm
9
Q
35
C
40
B
R
A
S
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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22. Determine the type of triangle if it has vertices at (5,4) and (7,12) and (13,6).
Measure the length of each side using distance formula or by making right triangles and using
Pythagorean theorem. Triangle is ISOSCELES because 2 sides are equal. 68, 68, 72
23. Find the area of an equilateral triangle whose sides are 6 cm each.
You must draw in the height of the triangle which creates two 30-60-90 triangles.
1
So height = 3 3 . Therefore the area = (6)(3 3)  9 3cm2
2
24. The base is a trapezoid where h = 9 cm.
Find the volume of the trapezoidal based pyramid.
1
Volume  (area of base)(  height)
3
1 1

Volume   (12  20)  9  24
3 2

3
Volume  1152cm
25. The surface area of the rectangular prism is 430 square inches.
Calculate the value for the side labeled x.
Find the area of each surface and they must add up to 430.
105  105  7 x  7 x  15 x  15 x  430
x5
26. Find the area of the shaded sector.
3
of total circle area
4
270
Area 
 (  92 )  190.755in 2
360
27. The lengths of the corresponding sides of two similar trapezoids are in the ratio 3:7. If the
area of the smaller trapezoid is 27 square inches, what is the area of the larger trapezoid?
Make sure you use the ratio 9:49 for area!! (not 3:7 b/c that is ONLY used for lengths)
area of the larger  147in2
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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28. A guy wire from the top of a telephone pole is anchored to the ground 19.2 m from the base
of the tower. The wire makes a 57 angle with the ground. To the nearest tenth of a meter,
what is the length of the guy wire?
19.2
This is a trig problem so draw a picture and be sure you use cosine.
w
w  35.2527  35.3m
cos57 
29. DEC is similar to what triangle?
Which Similarity conjecture confirms this?
AA Similarity ONLY b/c all the angles are congruent.
There is not enough information to show
the sides maintain the same ratio.
Kruzich 11 - Geometry Semester 2 Final Review – Answer Key
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