NAME:_________________________
St. Francis High School
Geometry Mastery Skills
Workbook
Use this workbook to help prepare for the Mastery Skills test that will be given
in the first week of school to all students enrolled in Advanced Algebra or
Honors Advanced Algebra Trig. The format of the test is multiple choice.
Do the first Practice Test – it contains samples of the types of problems on the test.
If you are having trouble with any section more problems can be found in the
following pages of the workbook or by searching the internet or in workbooks
available in bookstores. The test will be taken WITHOUT calculators. Answers are
provided at the back of the workbook. Work through the skill sections during the
summer.
A sample multiple choice test is included at the end of the workbook. Take this
sample test the week before schools starts and brush up on any sections that you
found difficult. You will be asked to do extra work on the skills you do not
successfully master. Good luck.
GEOMETRY MASTERY SKILLS PRACTICE
TEST
The test you will take on the first day of school has question similar to this test. You are not expected to get 100%, but
you should get most problems in each skill correct. Practice for this and you will start your year off right.
NO CALCULATOR!!!
SKILL G1: Parallel and Perpendicular Lines
1. Line k is parallel to line m.
2. Line k is parallel to line m.
If 1  2 x  5 , find the value of x.
If 1  2 x  15 and 2  3x  85 , find the measure
of 1 .
k
k
125°
2
1
m
1
m
4. Name the lines that must be parallel if 5  2
3. Given the figure, find the measure of x.
x
H
1 2 3
G
F
4
45°
55°
SKILL G2: Vocabulary
5. A and B are complementary angles.
If they are angles in a triangle, the
third angle measures _______
degrees.
L
8 7
K
6
J
ABC is isosceles with vertex C.
What is the perimeter?
B
6.
5
7.
AB bisects DAC . If BAC
equals 48°, then DAC
=______.
10
A
6
SKILL G3: Area, Perimeter, and Volume
8. Find the perimeter and area of the parallelogram.
15
C
9. Use the formula V = Bh to find the volume of the
cylinder pictured below.
13
5 cm
5
10. Use the formula V = Bh to find the volume of the
prism pictured below.
11. Use the formula Lateral Area =  rl
to find the lateral area of the cone pictured.
( l  slant height)
15 cm
8
5
6
6 cm
Geometry Mastery Skills Workbook
’14-‘15
p. 2
SKILL G4: Right Triangles
12. Find the length of the hypotenuse (leave in simplified
radical form):
13. Use trig to find x to the nearest tenth.
x
4
x
10
10
35°
14. From a point 65 feet from the base of a building, the
angle of elevation to the top of the building is 55◦. To
the nearest foot, how high is the building?
A
Solve for the two missing sides.
(Leave answer in radical form.)
15. Find the diagonal of a rectangle whose sides are 21
and 72.
18. What is the diagonal of a square if the side is 5?
16. AB =__________
17. AC=__________
B
SKILL G5: Radicals
60°
5
C
Simplify. Leave all answers in simplified radical form.
50  32
20.
19. 3 50
21. 5 2  3 15
22.
3 2
6
SKILL G6: Coordinate Geometry
y
E

23. Find the midpoint of DE

24. Find the distance
between the points.

D




25. What is the slope of DE
?

Geometry Mastery Skills Workbook
to DE ?_______
28. Find the coordinates of the point 3 units to
the right of point D. ______

x

26. What is the slope of the line parallel to DE
_______
27. What is the slope of the line perpendicular
’14-‘15
p. 3
29. Find the coordinates of the new point when
E is reflected over the y axis. _________
SKILL G7: Quadrilaterals
Always, Sometimes or Never?
32. ABCD is a parallelogram.
A  x , D  (2 x  6) .
Find C .
30. ______A trapezoid is a parallelogram.
A
B
31. ______A square is a rectangle.
C
D
33. ABCD is a parallelogram. AB = 2x + 3, BC = 6, CD =
x + 4. Find the perimeter of ABCD.
A
B
34. TRAP is a trapezoid. TP = 3x+2, TR= 5x-3, RA = 7x-6, AP =
6x+5. What value of x would make TRAP an isosceles
trapezoid?
T
C
D
R
E
P
SKILL G8: Similarity
Find the missing values.
ABC
A
37. Find the missing value.
XYZ
A
x
C
B
a
X
2
Y
15
8
5
8
12
y
Z
4
35. a =__________
36. y=__________
38. If the smallest sides of two similar triangles are 3
and 8 and the perimeter of the smaller triangle is
12, what is the perimeter of the larger triangle?
Geometry Mastery Skills Workbook
’14-‘15
x=__________
39. The blueprint of a bedroom in a new house measures 4
inches by 5 inches. If the larger dimension of the
bedroom is actually 15 feet, how many square feet of
carpet will I need?
p. 4
MASTERY SKILLS PRACTICE SECTIONS
SKILL G1: PARALLEL AND PERPENDICULAR LINES
 Definition of parallel – two lines in a plane that will never intersect
 Definition of perpendicular – two lines that intersect to make right angles
 Given two parallel lines and a transversal,
o Alternate Interior(Z), Alternate Exterior and Corresponding (F) angles are congruent
o Same-side Interior (U)and Same-side Exterior are supplementary
1. Given the figure, find the
2. Given the figure, find the measure
3. Given the figure, find the
measure of x.
of x.
measure of x.
x
120°
x
x
155°
70°
4. Given the figure, find the
measure of x.
5. Given the figure, find the measure
of x.
6. Given the figure, find the
measure of x.
x
(x+20)°
85°
x
42°
130°
7. Line k is parallel to line m. If
1  2 x  3 , find the value of x.
8. Line k is parallel to line m. If
1  3x  7 , find the value of x.
m
125°
9. Line k is parallel to line m. If
1  3x  28 and 2  5 x  72
, find the value of x.
m
56°
m
1
1
k
k
1
k
2
Geometry Mastery Skills Workbook
’14-‘15
p. 5
10. Line k is parallel to line m. If
1  2 x  17 and
2  4 x  37 find the value of
1 .
11. Line k is parallel to line m. If
1  3x  28 and 2  4 x  85
find the measure of  2 .
12. Line k is parallel to line m. Find
the value of  2 .
(5x+8)°
m
2
m
2
(7x-32)°
m
2
1
1
k
k
k
13. Given the figure, find the
measure of x.
x
50°
14. You have traveled 3 miles on Road A
and then turn onto Road B which is
perpendicular to Road A. You travel 4
miles on Road B and stop. What is the
distance between your starting point
and stopping point?
15. Given the figure, find the
measure of x.
63°
60°
16. In triangle ABC, AB is
perpendicular to BC . If
ACB is 68°, find the measure
of BAC
17. Name the lines that must be
parallel if 4  1
G
L
Given the figure, find the missing
angles.
4
1
H
1 2 3
8 7
K
x
18. . Name the lines that must be
parallel if 1  7
G
4
6
H
1 2 3
F
4
5
J
L
8 7
K
6
5
J
19. If 1 =105°, 3 =_____
22. If  4 =120°, 3 =_____
20. If  2 =65°,  4 =_____
23. If  2 =70°, 1 =_____
21. If 5 =110°,  4 =_____
24. If 1 =130°, 5 =_____
2
5
3
Geometry Mastery Skills Workbook
F
147°
’14-‘15
p. 6
SKILL G2: VOCABULARY
 Supplementary (two angle sum of 180°) and Complementary (two angle sum of 90°)
 Midpoints and Bisectors divide a segment or angle into 2 congruent parts.
 Triangles:
o acute (all angles between 0° and 90°), obtuse (one angle between 90° and 180°), right (one angle = 90°)
o Scalene (no sides congruent), isosceles (at least 2 sides congruent), equilateral (all sides congruent)
o Congruent – all corresponding angles and sides are congruent
 Polygon names (# sides): Triangle (3), Quadrilateral (4), Pentagon (5), Hexagon (6), Octagon (8), Decagon (10)
o Interior angles sum: S = (n-2)180°
S= angle sum
o Exterior angle sum is ALWAYS 360°
n= number of sides or
o Interior angle and Exterior angle are supplementary
angles
360
360
o Each exterior angle of a REGULAR polygon: E 
or n 
E = one exterior angle
n
E
d= number of diagonals
n(n  3)
o Number of diagonals: d 
2


Circle: center, radius, chord, diameter, secant, tangent, central angle, inscribed angle
Solids:
o Prisms (two parallel polygonal bases, lateral faces are rectangles)
o Cylinder (two parallel circular bases)
o Pyramid (one square or equilateral triangular base, lateral faces are isosceles triangles)
o Cone (one circular base with vertex directly above the center of the base)
Sample Problems:
1. Fill in the following table:
2. One of two complementary angles What is the measure of each
is 40° more than the other. What
exterior angle of a regular:
Angle Complement Supplement
is the measure of the larger angle?
A 17°
3. hexagon
B 50°
C
42°
D
71°
4. decagon
E
112°
F
165°
7.
A triangle has angles that measure 2x, 5x, and x + 20.
ABC is isosceles with vertex A. What is the
perimeter?
B
10
5. Is this triangle acute, obtuse, or right?
6. Is this triangle scalene, isosceles or equilateral?
8. What is the measure of each interior angle of a regular
decagon?
Geometry Mastery Skills Workbook
’14-‘15
A
8
9. How many diagonals does an octagon have?
p. 7
C
Use the following words to answer # 11-30. Words may be used more than once or not at all.
Central angle
Diameter
Isosceles Trapezoid
Radius
Scalene
Center
Equiangular
Kite
Rectangle
Slant height
Chord
Height
Obtuse
Regular
Square
Cone
Inscribed angle
Prism
Rhombus
Tangent
Cylinder
Isosceles
Pyramid
Secant
Triangle
10. Does P inscribe or
Give the best name for:
circumscribe the
18. This solid is a _______________
12. DC
A
quadrilateral?
19. AC is the ________
D
13. DC
__________.
•
14. P
20. AP is the ___________
P
A
P
B
15. DB
11. Below is an example
C
of_______
16. PD
17. AB
B
P
21. The lateral faces of a _____________ are isosceles triangles.
22. The bases of a ________________ are always congurent circles.
23. A(n) __________________angle in a circle equals half the measure of its arc.
24. All equilateral triangles are _______________________.
25. A triangle with no sides congruent is __________________.
26. A triangle with one angle larger than 90° is ______________.
27. An equiangular quadrilateral must be a ___________________.
28. An equilateral quadrilateral must be a ___________________.
29. A polygon with all sides congruent and all angles congruent is a ______________ polygon.
30. The sum of the angles of a ____________ is 180°.
Fill in the blanks.
31. A and B are complementary angles. If they are angles in a triangle, the third angle measures _______ degrees.
32. How many faces does a square pyramid have? ________
33. Can a triangle be isosceles and right? _______
34. In circle P, If LAPC = 35°, then AC = ______.
35. The longest side of a right triangle is the ________________.
A
36. AB bisects DAC . If BAC equals 68°, then DAC =______.
37. What is a name for the parallogram at the right? AB__ __
Geometry Mastery Skills Workbook
’14-‘15
p. 8
C
B
D
C
SKILL G3: AREA, PERIMETER, AND VOLUME
Find the area and perimeter of each figure. Leave
1. Triangle

in the answer.
2. Triangle
10
24
10
3. Circle P.
4. Find the area of a circle if the perimeter is 12π
P
3
5. Rectangle
6. Rectangle
4
7
7. Find the area of triangle ABC
8. Find the area and perimeter of the Parallelogram.
A
4
1
13
3
10
B
C
10
Geometry Mastery Skills Workbook
5
’14-‘15
p. 9
Problems 9 through 26 use the following symbols:
B = area of the Base h = height of the solid
9. The formula for volume of a right cylinder is
Volume = πr2h
r = radius of circular base l = slant height
10. Use the formula from problem #9 to find the
volume of the cylinder pictured below.
Use this formula to find the volume of the cylinder
pictured below.
12
11
9
6
11. The formula for volume of a right prism is
Volume = Bh
12. Use the formula from problem #11 to find the
volume of the prism pictured below.
Use this formula to find the volume of the prism
pictured below.
F
A
5
15
10
20
B
18
Geometry Mastery Skills Workbook
’14-‘15
p. 10
3
C
13. The formula for volume of a right cone is
Volume =
14. The formula for lateral area of a cone is
1 2
r h
3
Lateral Area =  rl
Use this formula to find the lateral area of the
cone pictured.
Use this formula to find the volume of the cone
pictured below:
12
5
15. The formula for volume of a right pyramid is
Volume =
1
Bh
3
16. Use the formula from problem #15 to find the
volume of the pyramid pictured below.
Use this formula to find the volume of the pyramid
pictured below.
h = 6 cm
h =5 cm
w = 8 cm
l = 10 cm
w =6 cm
l = 8 cm
17. The formula for volume of a sphere is
4
Volume   r 3
3
18. Use the formula from problem #17 to find the
Volume of the sphere pictured below:
Use this formula to find the volume of the sphere
pictured below:
r=9m
Geometry Mastery Skills Workbook
’14-‘15
p. 11
SKILL G4: RIGHT TRIANGLES
Pythagorean Theorem
Right Triangle- Families (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25)
30-60-90, 45-45-90 Triangles
SOH – CAH – TOA
1. Find the length of the
2. Find the length of the hypotenuse
hypotenuse:
(leave in radical form):
x
15
3. Find the length of the missing leg:
25
x
12
20
24
24
4. Find the length of the missing leg:
Using opp (opposite), adj (adjacent)
and hyp (hypotenuse), define these
trig ratios:
5. A ladder 6.0 meters long rests
against the sill of a second-story
window. The base of the ladder is
3.6 meters from the base of the
wall). How far is the window sill
above the ground?
Given this triangle ABC, give the
trig ratios:
6. A kite gets caught in the top of a
tree. The string is 65ft. long. The
boy is holding the string 60 ft.
from the base of the tree, how tall
is the tree?
Find the length of x in the triangle
below:
7. Sin x =
8. Cos x =
10. sin B =
11. cos C =
9. Tan x =
13. x =
12. tan C =
Geometry Mastery Skills Workbook
’14-‘15
x
p. 12
14. From a point 78 feet from the
base of a building, the angle of
elevation to the top of the
building is 57 degrees. To the
nearest foot, how high is the
building?
15. Given right triangle ABC. The
tangent of angle A is 4/3. The
length of the side opposite A is 12.
What are the lengths of the other
2 sides?
16. The measure of angle A is 30
degrees, and side b is 8. What is
side a? (Leave answer in radical
form)
17. Find the diagonal of a rectangle
whose side s are 24 and 32.
18. Solve for the two sides.
19. Solve for the two sides. (Leave
answer in radical form)
8
20. Solve for the two sides.
Geometry Mastery Skills Workbook
3
5 3
21.
’14-‘15
22. The angle of depression from the
top a lighthouse on the shore to a
ship at sea is 32°. If the lighthouse
is 30 ft. high, how far, to the
nearest foot, is the ship from the
shore?
p. 13
SKILL G5: RADICALS
Radicals
a. Simplify
b. Addition and Multiplication
c. Rationalize
Simplify. Leave all answers in simplified radical form.
1.
80
4.
6 18
7.
3 5 5
2.
75
3.
a6
6 45x 5
6.
3y 24y 9
8. 2 6  7 6
9.
4 12  8 27
10. 3 9  5 8  2 4
11. 11 18  72  4 45
12. 2 16  5 20  6 12
13. 3 18  4 14  5 8
14. 3 6  6 3
15.
Geometry Mastery Skills Workbook
5.
’14-‘15
p. 14
5 5
16.
11  3
19. 2 5  4 6
22.
25.
36
12
5
36
28.
17.
20.
7 8

3 2 3 5 7
18.

23.
24.
26.
5
2
2 3
6
27.
8 3
20
Geometry Mastery Skills Workbook

4 6 3 7 9 2
45
5
30.
29.
21.
10  5
4
25
32.
5 2
5
8 6
2 2
31.
’14-‘15
33.
p. 15

SKILL G6: COORDINATE GEOMETRY
Coordinate Geometry
 Reflection of point over an axis
 Coordinates of points on vertical or horizontal lines
 Midpoint formula
 Distance formula
 Slopes of parallel or perpendicular lines
1. Find the coordinates of the point
3 units directly above (–3,–5)
2. Find the coordinates of the point
3 units directly to the right of
(–3,–5)
3. Find the coordinates of the point 4
units to the right and 6 units down
from (–3,–5)
4. Find the coordinates of the new 5. Find the coordinates of the new
point when (2,5) is reflected over
point when (3, –2) is reflected
the x-axis.
over the x-axis.
6. Find the coordinates of the new
point when (7, –4) is reflected over
the x-axis
7. Find the coordinates of the new 8. Find the coordinates of the new
point when (2,5) is reflected over
point when (3, –2) is reflected
the y-axis.
over the y-axis
9. Find the coordinates of the new
point when (7, –4) is reflected over
the y-axis
10. Find the midpoint between
(–3,6) and (8,–5)
11. Find the distance between
(–3,6) and (8,–5)
12. Find the slope between (–3,6)
and (8,–5)
13. Find the midpoint between
(0,2) and (8,4)
14. Find the distance between
(0,2) and (8,4)
15. Find the slope between (0,2)
and (8,4)
Geometry Mastery Skills Workbook
’14-‘15
p. 16
16. Find the midpoint between
(8,–6) and (8,10)
17. Find the distance between
(8,–6) and (8,10)
18. Find the slope between
(8,–6) and (8,10)
Given the following
A (-1,3) 
y
19. Find the slope between the points.

20. Find the midpoint

x








21. Find the distance between the points



22. What is the slope of the line parallel to AB ?
B (2,-2)

23. What is the slope of the line perpendicular to AB ?
Given the following

y
24. Find the slope between the points.
E(4,3)

25. Find the midpoint

D(–2,1)
26. Find the distance between the points

x









27. What is the slope of the line parallel to ED ?

28. What is the slope of the line perpendicular to ED ?
Geometry Mastery Skills Workbook
’14-‘15
p. 17
SKILL G7: QUADRILATERALS
1.
2.
3.
4.
5.
Quadrilateral Family Tree
Opposite angles of a parallelogram are
____________________.
Diagonals of a Rectangle are
________________________.
Diagonals of a Rhombus are
___________________.
If TRAP is an isosceles trapezoid, what can you
say about LP and LR? __________________
What can you say about quadrilateral QUAD If
Q
Angle sum is 360°
P
K
diag. bis. ea. other
consec. angles supp
opp. angles congruent
QA is  bisector of UD ?
6.
7.
8.
9.
__________________
Does a rectangle have opposite sides
congruent? ____
Are the diagonals of the isosceles trapezoid
bisectors of each other? _____
Name three quadrilaterals that will always
have congruent diagonals.
______________________
A parallelogram is (Always, Sometimes, Never)
a rectangle.
T
IT
Rh
R
diag. perpendicular
diag. bis angles
diag. congruent
diag. congruent
ALWAYS
S
SOMETIMES
R & Rh
NEVER
10. A square is (Always, Sometimes, Never) a
rhombus.
IN EACH OF THE FOLLOWING PROBLEMS ABCD IS A PARALLELOGRAM.
11. AD = x + 5, AB = x + 9, BC = 2x + 12. LA = x°, LD = (3x-4)°. Find LC
1
Find DC.
A
B
A
A
B
D
C
Geometry Mastery Skills Workbook
’14-‘15
B
C
D
D
13. In order for ABCD to be a
rectangle, what must the value
of x be if LADB = (2x + 6)° and
LBDC=42°?
p. 18
C
REMEMBER: ABCD is a parallelogram.
14.
AB = 2x + 6, BC = 8, CD = x + 8.
Find the perimeter of ABCD.
A
B
15. AB = 3x + 4, BC = 5x – 2,
16. AD = y + 4, and BC = 3y – 8. The
DC = x + 10, and LAEB = (5y – 20) °.
perimeter is 40. What is the
What value of x and y would make
best name for ABCD?
ABCD a square?
A
B
A
E
C
D
B
C
D
Work each of the following problems.
17. KITE is a kite. KI=10, IT=17, and
KA=6. Find KT.
I
K
A
C
D
18. TRAP is a trapezoid. TP = 5x – 2
and RA = 3x + 10. What value of
x would make TRAP an isosceles
trapezoid?
T
R
19. TRAP is an isosceles trapezoid.
PE = x + 5, ER = 2x – 1, TA = 13.
Find PE
T
R
E
T
E
P
P
E
Geometry Mastery Skills Workbook
’14-‘15
A
p. 19
A
SKILL G8: SIMILARITY
 Triangle proportions
 Scale factor
Find the missing values for the similar figures below.
1.
ABC
2.
XYZ
X
c
6
5
3
B
4
a=__________
c=__________
3.
Y
8
3
a
y
2
A
C
a
a=__________
4.
ABC
Z
4
y=__________
XYZ
C
b
10
b
c
15
A
13
x
Z
Y
4
10
X
5
12
B
b=__________
c=__________
5.
b=__________
x=__________
6.
5
10
5
25
6
x
x=__________
Geometry Mastery Skills Workbook
x=__________
’14-‘15
p. 20
7
x
7.
8.
x
12
3
12
x
8
5
6
x=__________
x=__________
9.
10.
4
12
26
3
5
x
9
x
x=__________
11. If the side ratio of two similar
figures is 2:3, what is the
perimeter ratio?
x=__________
12. If the perimeter ratio of two
similar figures is 3:4, what is the
Area ratio?
14. If the smallest sides of two similar triangles are 6
and 10 and the perimeter of the smaller triangle is
24, what is the perimeter of the larger triangle?
Geometry Mastery Skills Workbook
’14-‘15
13. If the Area ratio of two similar
figures is 36:25, what is the
perimeter ratio?
15. If two triangles are similar and the smallest sides are 6
and 10 and the Area of the larger triangle is 200, what
is the area of the smaller triangle?
p. 21
Solve the following scale factor problems.
16. The scale on a map is 1 inch equals 10 miles. If the
distance from Chicago to Wheaton on the map is 3.5
inches, how far apart are the cities?
17. The floor plan of my room in our new house is 2 inches
by 3 inches. If the smaller dimension is really 8 feet,
how many square feet of carpet will I need?
18. The John Hancock Building in Chicago is 459 meters
tall. If the Lego store in Schaumburg wanted to
build a scale model of the Hancock Building using
the scale of 3m:2cm, how tall would the scale model
be?
19. A model airplane has a wing span of 3 inches and a
length (nose to tail) of 9.5 inches. If the real airplane is
200 meters long, what is its wingspan rounded to the
nearest tenth?
20. Walter E. Smythe is furnishing your living room. You
have to bring a scale drawing of this room to your
designer. If a wall that is actually 20 ft., is drawn as
5 inches in your drawing, how long should your 15
foot wall be in your drawing?
21. Two similar garden plots have a perimeter ratio of 2:3.
If the area of the smaller garden is 160 square ft. ,
what is the area of the larger garden?
Geometry Mastery Skills Workbook
’14-‘15
p. 22
GEOMETRY MASTERY SKILLS PRACTICE TEST
MULTIPLE CHOICE
TESTTETESTTETESTTESTTEST
The test you take the first week of school is very similar to this test. You should get most problems in each skill correct.
Practice for this and you will start your year off right.
NO CALCULATORS
SKILL G1: Parallel and Perpendicular Lines
1. Given the figure, find the measure 2. Line k is parallel to line m.
of x.
1  5x  15 and
2  4 x  20 Find the value of
x
x.
k
42°
m
53°
3. Line k is parallel to line m.
If 1  2 x  15 , find the value of
x.
k
1
135°
2
1
m
a) 96°
b) 65°
a) 15
b) 40
a) 30
b) 60
c) 74°
d) 85°
c) 5
d) 90
c) 45
d) 15
SKILL G2: Vocabulary
4. One of two supplementary angles
is 30 more than the other. What
is the measure of the smaller
angle?
5.
ABC is isosceles with vertex C.
What is the perimeter?
6.
XY and XV trisect WXZ . If
YXV equals 50°, then WXZ
=______.
14
12
a) 150°
b) 105°
a) 38
b) 12
a) 50°
b) 100°
c) 15°
d) 75°
c) 40
d) 14
c) 150°
d) cannot be
determined
Geometry Mastery Skills Workbook
’14-‘15
p. 23
SKILL G3: Area, Perimeter, and Volume
7. Find the area of the
8. Use the formula V = Bh to find
parallelogram.
the volume of the cylinder
pictured below.
18
5 cm
9. Use the formula
Lateral Area =  rl
to find the lateral area of the
cone pictured.
( l  slant height)
10
10 cm
6
12
9
a) 144
b) 180
a) 250π
b) 100π
a) 108π
b) 135π
c) 60
d) 56
c) 50π
d) 150π
c) 972π
d) 1205π
SKILL G4: Right Triangles
10. Find the length of the hypotenuse
(leave in simplified radical form):
11. Find the measure of AC.
12. Find the diagonal of a rectangle
whose sides are 4 and 10.
A
x
4
30°
18
6
B
a) 2 5
b) 2 13
a) 9 2
c)
d)
c) 9 3
20
52
Geometry Mastery Skills Workbook
’14-‘15
C
b) 9
a) 2 21
c)
p. 24
14
b) 2 29
13. Write the trig equation used to find x.
14. From a point 30 feet from the base of a building, the
angle of elevation to the top of the building is 25◦.
Write the trig equation used to find the height of the
building.
8
55°
x
a)
c)
x
8
8
tan 55 
x
cos 55 
b)
d)
SKILL G5: Radicals
x
8
8
cos 55 
x
sin 55 
a)
c)
30
h
h
tan25 
30
tan25 
b)
d)
h
30
30
cos 25 
h
sin 25 
Simplify. Leave all answers in simplified radical form.
15. 3 24
90  40
16.
a)
2 6
b)
12 6
a)
130
c)
6 6
d)
6 3
c)
13 10
b)
5 10
17.
2 3
2
a)
6
c)
3
b)
6
2
SKILL G6: Coordinate Geometry
19. Find the distance between D and E.
y


20. Find the coordinates of the point
2 units to the left of point E.
E

a) (1, 5)
b) (-1, 3)
c) (-4, -1)
d) (4, 3)

x

D


21. What is the slope of the line
parallel to DE ?



18. Find the midpoint of DE
a) (0, 1.5)
b) (-1.5, 1)
a) 5
c) (-0.5, 1)
d) (1.5, 0)
c)
Geometry Mastery Skills Workbook
’14-‘15
b)
5
7
a)
c)
p. 25
3
4
4
3
b)
d)
2
1
4
3
SKILL G7: Quadrilaterals
22. ABCD is a parallelogram.
D  11x  10  , B  (20 x  26)
.
Find A .
A
23. RHOM is a rhombus. If
RDH  7 x  8 , what is the
value of x?
B
A
R
M
24. ABCD is a parallelogram.
AD = 3x – 4, BC = 5, CD = x + 4.
Find the perimeter of ABCD.
B
D
D
C
D
O
82
7
a) 54°
b) 126°
a) 14
c) 4°
d) 176°
c) not enough information
SKILL G8: Similarity
25. Find the value of x.
6
18
C
H
b)
26. ABC XYZ
AB=5, AC= 10, BC = 4, XY=3.
Find XZ.
x
6
a) 7
b) 12
c) 3
d) 24
27. If the smallest sides of two
similar triangles are 3 and 8 and
the perimeter of the smaller
triangle is 21, what is the
perimeter of the larger triangle?
28
a) 14
b) 7
c) 9.3
Geometry Mastery Skills Workbook
a) 16.6
b) 2.4
c) 6
’14-‘15
p. 26
a) 32
b) 7.875
c) 56
d) not enough information
ANSWERS
PRACTICE TEST
1. 30
2. 125°
3. 80°
6. 22
11. 60π
7. 96
12. 2 29
8. 56, 180
13. 17.4
16. 10
17. 5 3
21. 15 30
22.
3
2
31. Always
16
36.
or 3.2
5
26.
3
2
3
32. 62
37. 10
27.
4. HK , FJ
9. 720π
14. 93
5. 90
18. 5 2
23. (0, 2.5)
19. 15 2
28. (2, 1)
29. (–1, 4)
20. 9 2
3
25.
2
30. Never
33. 22
38. 32
34. 2
39. 180
SKILL G1: Parallel and Perpendicular lines.
1. 70
2. 60
3. 155
9. 22
10. 59
11. 143
17. KH / / JF 18. KJ / / HF 19. 105
SKILL G2: Vocabulary
1A. 73, 163
1B. 40, 130
2. 65
3. 60
8. 144
9. 20
14. Center
15. Chord
20. Height
21. Pyramid
25. Scalene
26. Obtuse
31.
90
32. 5
33. Yes
SKILL G3: Area, Perimeter, and Volume
1. A=120, p=60
2. A=192, p=64
6. A=480, p=92
7. A=20
11. V = 2160
12. V = 60
16. V=160
17. V=972π
SKILL G4: Right Triangles
1. 25
2. 12 5
opp
adj
17. 40
9.
b
a
18. AC=10
BC=5
10.
3. 7
11.
12.
19. AB = 8 3
BC = 8
Geometry Mastery Skills Workbook
5. 85
13. 70
21. 110
’14-‘15
c
b
35. 10
6. 48
14. 5
22. 120
1D. 19, 161
5. Obtuse
11. Prism
17. Tangent
23. Inscribed
28. rhombus
35. Hypotenuse
3. A=9π, p=6π
8. A=132, p=48
13. V=12π
2048
18. V 

3
4. 10
b
a
24. 13
4. 30
12. 72
20. 115
1C. 48, 132
4. 36
10. Circumscribe
16. Radius
22. Cylinder
27. rectangle
34. 35
10. 180
15. 75
8. 39
16. 22
24. 130
1E. 68, 22
1F. 15, 75
6. Isosceles
7. 26
12. Secant
13. Diameter
18. Cone
19. Slant height
24. Isosceles or equiangular
29. regular
30. triangle
36.
136
37. DC
4. A=36π
9. V=396π
14. V=65π
5. 4.8
6. 25
13. 8
14. 120
20. AC=4
BC=4
21. 56
p. 27
7. 29
15. 57
23. 110
5. A=28, p=22
10. V=972π
15. V= 80
opp
hyp
15. AC=9
AB=15
7.
22. 48
8.
adj
hyp
16. 8 3
SKILL G5: Radicals
1. 4 5
2. 5 3
9. 32 3
20. 6  5 21
10
2
26.
4. 18 2
14. 54 2
11. 39 2  12 5
15. 5
16. 33
10. 5  10 2
2  4 14
13.
3. a3
21. 12 42  72 3
27.
2
28.
22.
29. 10
4 15
5
SKILL G6: Coordinate Geometry
1. (-3, -2)
2. (0, -5)
3. (1, -11)
8. (-3, -2)
9. (-7, -4)
10. (2.5, 0.5)
15.
16. (8, 2)
1
4
22. 
5
3
23.
3
5
24.
1
3
SKILL G7: Quadrilaterals
1. 
2. 
3. 
8. IT, R, S
9. Sometimes 10. Always
15. x=3, y=22
16. rhombus
17. 21
SKILL G8: Similarity
1. a=8, c=10
6. 35
11. 2:3
16. 35
21. 360
2. a=6, y= 16/3
7. 7.5
12. 9:16
17. 96
Multiple Choice Practice Test
1. D
2. C
8. A
9. B
15. C
16. B
22. B
23. A
3. D
10. B
17. A
24. D
Geometry Mastery Skills Workbook
’14-‘15
8. 5 6
7. 4 5
12. 8  10 5  12 3
17. 2 14
23. 3
3
18. 5 2
2
24.
5
19. 8 30
25.
5
6
30. 4 3
4. (2, -5)
11. 11 2
18. None
(vertical line)
25. (1, 2)
17. 16
6. 6 y 5 6 y
5. 18 x 2 5 x
5. (3, 2)
12. –1
6. (7, 4)
13. (4, 3)
7. (-2, 5)
14. 2 17
5
3
26. 2 10
20. (0.5, 0.5)
21.
19. 
4. P  R
11. 13
18. 6
3. b=24, c=26
8. 8
13. 6:5
18. 306
4. D
11. C
18. C
25. B
5. Kite
12. 46
19. 8
28. 3
1
3
6. Yes
13. 21
4. b=12.5, x=12
9. 10
14. 40
19. 63.2
5. C
12. B
19. A
26. C
p. 28
27.
6. C
13. A
20. B
27. C
34
7. No
14. 36
5. 12
10. 8
15. 72
20. 3.75
7. A
14. C
21. D