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by Jenny Paden, jenny.paden@fpsmail.org
1A
Draw segment AB and ray CD
A
C
B
D

1B
Name a four coplanar points
Points A, B, C, D
1C
Name a pair of opposite rays:
CB and CD
2A
M is the midpoint of PR,
PM = 2x + 5 and MR = 4x – 7.
Solve for x.
x=6
2B
3x
4x + 8
29
Solve for x
x=3
2C
E
6x – 4
F
3x
5x + 8
E, F and G represent
mile markers along a
straight highway. Find
EF.
EF = 14
G
3A
L is in the interior of  JKM.
Find m JKM if m  JKL = 32º
and m LKM = 47o.
mJKM = 79o
3B
BD bisects ABC,
m ABD = (4x - 3)º, and
m  DBC = (2x + 7)º.
Find m  ABD.
m  ABD = 17
3C
QS bisects PQR,
m  PQS = (2y + 1)º, and
m  PQR = (y + 12)º.
Find y.
y = 10/3 = 3.3
4A
1 2
Angles 1 and 2 are called:
A. Vertical Angles
B. Adjacent Angles
C. Linear Pair
D. Complementary Angles
B. Adjacent Angles
4B
1
2
Angles 1 and 2 are called:
A. Vertical Angles
B. Adjacent Angles
C. Linear Pair
D. Complementary Angles
A. Vertical Angles
4C
1
2
Angles 1 and 2 are:
A. Adjacent
B. Linear Pair
C. Adjacent and Linear Pair
D. Neither
C. Adjacent and Linear Pair
5A
The supplement of a 84o
angle is _____o
96o
5B
The complement of a 84o
angle is _____o
6o
5C
37.2o
Find the complement of the
angle above.
52.8o
6A
Find the perimeter and area of a
square with side length of 5 inches
Perimeter: 20 inches
Area: 25 inches2
6B
14
6
12
What is the perimeter and
area of the triangle above?
Perimeter = 32
Area = 36
6C
Find the circumference and
area of a circle with a
diameter of 10. Round your
answer to the nearest tenth.
Circumference: 31.4
Area: 78.5
7A
State the Distance Formula
 x2  x1    y2  y1 
2
2
7B
Find the distance of
(-1, 1) and (-3, -4)
29  5.39
7C
Find the length of FG
Answer: 5
8A
Find the midpoint of
(-4, 1) and (2, 9)
(-1, 5)
8B
Find the midpoint of
(3, 2) and (-1, 4)
(1,3)
8C
Find the midpoint of
(6, -3) and (10, -9)
(8, -6)
9A
BC and JE are called _____ lines:
A. Perpendicular
B. Parallel
C. Skew
D. Coplanar
Answer: C. Skew
9B
BF and FJ are _______.
A. Perpendicular
B. Parallel
C. Skew
A. Perpendicular
9C
BF and EJ are _______.
A. Perpendicular
B. Parallel
C. Skew
B. Parallel
10A
1
2
 1 and  2 are called _____ angles.
A. Alternate Interior
B. Corresponding
 B. Corr.
C. Alternate Exterior
D. Same Side Interior
10B
x°
Find x.
48°
x = 132o
10C
Find the
measure of
each angle.
1 = 115o,  2 = 115o
 3 = 148o,  4 = 148o
11A
Find x.
x = 22
11B
6x +10
4x + 20
Find x.
x = 15
11C
6x +10
4x + 20
Find x.
x=5
12A
Given line
segment XY,
what construction
is shown:
Perpendicular Bisector
12B
a)Name the shortest segment
from A to CB
b)Write an inequality for x.
a) AP
b) x > 20
12C
a) Name the shortest segment
from A to CB
b) Write an inequality for x.
a) AB
b) x < 17
13A
Classify the triangle
by its angles AND
sides.
Acute isocseles
13B
Classify the
triangle by its
angles AND
sides.
Equilateral and Equiangular
(or Acute)
13C
Classify the
triangle by its
angles AND
sides.
Obtuse Isosceles
120º
30º
14A
Find y.
y=7
14B A manufacturer produces musical
triangles by bending steal into the
shape of an equilateral triangle.
How many 3 inch triangles can
the manufacturer produce from a
100 inch piece of steel?
11 Triangles
14C
Find the length of JL.
JL = 44.5
15A
115º
36º
Find x.
x = 29
xº
15B
47
Find x.
x = 74
27
x
15C
4x + 10°
Find x.
5x - 60°
x = 22
x + 10°
16A
A
Triangles ABC  DEF
Find x.
D
43o
47o
B
C
2x + 3 = 47
2x = 44
x = 22
2x +3
E
F
16B
The triangles are congruent.
Find x.
x=4
16C
Find y.
y = 64o
17A
Name the five “Shortcuts”
to Proving Triangles are
Congruent.
SSS, SAS, ASA, AAS, and HL
17B
Are the triangles
congruent? If so,
state the
congruence
theorem to
explain why
triangles are
congruent.
Yes, AAS
17C
Are the triangles
congruent? If so,
state the
congruence
theorem to
explain why
triangles are
congruent.
Yes, SSS
18A
What does CPCTC stand for?
Corresponding Parts of
Congruent Triangles are
Congruent
18B
Yes, CPCTC
18C
Given the triangles, is A  P?
Yes, CPCTC
19A
Find x
x = 70o
19B
Find x.
x = 72o
19C
Find x.
x = 14
20A
Which Property of Equality is
shown here?
2x + 3 = 10
2x = 7
Subtraction Property of
Equality
20B
Which Property of Equality is shown here?
2x = 10
x=5
Division Property of Equality
20C
Write a two column Proof
for the following Algebra
Equation.
3(t – 5) = 39
Statements
1. 3(t-5)=39
2. 3t – 15 = 39
3. 3t = 54
4. t = 18
Reasons
1. Given
2. Distributive
3. Addition Prop. Of Equal.
4. Division Prop. Of Equal.
21A
Identify the property that
justifies the following
statement.
DC  DC
Reflexive Property of Congruence
21B
Identify the property that justifies
the following statement.
m1  m2,
and
m2  m3. So m1  m3
Transitive Property of Equality
21C
a = b, so b = a
Symmetric Property of Equality
22A
Complete the following proof
Given:  KLJ   MLJ ,  K   M
Prove: KL  ML
Statements
Reason
1.  KLJ   MLJ ,  K   M 1. Given
2.
3.
JL  JL
KLJ  MLJ
4. KL  ML
2. Reflexive
3. AAS
4. CPCTC
22B
Complete the following proof
Given: B is the midpoint of DC
AD  AC
Prove:
DAB  CAB
Statements
D
Reasons
A
B
1. B is the midpoint of DC 1. Given
2.
DB  BC
2. Def of Midpoint
3.
BA  BA
3. Reflexive
4. AD  AC
4. Given
5. DAB  CAB
5. SSS
C
22C
Complete the missing statements.
Given: W is the midpnt of XZ , XY  ZY
Prove:  X   Z
Statements
Reasons
1. W is the midpnt of XZ 1. Given
2. XW  WZ
2. Def of Midpoint
3. XY  ZY
3. Given
4.
4. Reflexive
WY  WY
5. WYX  WZY
6.  X   Z
5. SSS
6. CPCTC
Type answer here
23A
Find x and UT
x = 6.5, UT = 28.5
23B
Find a and mMKL
a = 6, mMKL = 38o
23C
Fill in the Blank.
The Perpendicular Bisector Theorem
If a point is on the perpendicular
bisector of a segment, then it is
__________ from the endpoints of the
segment.
Equidistant
24A
Find GC.
13.4
24B
Find GM.
14.5
24C
Segments QX and RX are angle
bisectors. Find the distance from
x to PQ
19.2
25A
Fill in the blank.
A _____________ of a triangle is a segment
whose endpoints are a vertex of the
triangle and the midpoint of the opposite
side.
A.
B.
C.
D.
Altitude
Median  Median
Angle Bisector
Perpendicular Bisector
25B
In ∆LMN, S is the Centroid of the triangle.
RL = 21 and SQ =4. Find LS.
LS = 14
25C
Z is the Centorid of the triangle.
In ∆JKL, ZW = 7, and LX = 8.1. Find KW.
1
1
KW = 21
26A
Given that DE is the midsegment find the length of AC
A
D
7 in.
C
14 inches
E
B
26B
Find mEFD
o
26
26C
Find the value of n.
2(n + 14) = 3n + 12
2n + 28 = 3n + 12
n = 16
27A
Write the angles in order
from smallest to largest.
F , H , G
27B
Write the sides in order
from shortest to longest.
mR = 180° – (60° + 72°) =
48°
PQ, QR, PR
27C
Tell whether a triangle can have
sides with the given lengths.
Explain.
7, 10, 21
No:
7+10 = 17 NOT greater than 21
28A
Compare mBAC and mDAC.
mBAC > mDAC
28B
Compare EF and FG.
mGHF = 180° – 82° =
98°
EF < GF
28C
Find the range of values for k.
5k – 12 < 38
k < 10
5k – 12 > 0
k < 2.4
29A
Simplify the radical
24
2 6
29B
Simplify the radical
12
2
4 3 2 3

 3
2
2
29C
Simplify the radical
200
100  2  10 2
30A
Simplify the radical
3
8
3 8
24
4 6 2 6
6




 
8
8
8
4
8 8
30B
Simplify the radical
4 3
2
 4 3  4 3   16 3  48
30C
Simplify the radical
 5 


 3
2
 5  5  25

   3
 3  3 
31A
Find the value of x. Leave your
answer in simplified form.
a2+ b2 = c2
22 + 62 = x2
4 + 36 = x2
40 = x2
40  4 10  2 10
31B
Find the value of x. Leave
your answer in simplified
form.
x
a2+ b2 = c2
52 + 122 = x2
25 + 144 = x2
169 = x2
13 = x
31C
Find the value of x. Leave your
answer in simplified form.
a2+ b2 = c2
52 + x2 = 102
25 + x2 = 100
X2 = 75
25 3  5 3
x
10
5
if the measures can be the side
32A Tell
lengths of a triangle. If so, classify the
triangle as acute, obtuse, or right.
7, 12, 16
a2
122
?
+
b2
= c2
+
?
2
7 =
162
?
144 + 49 = 256
193 < 256
Since a2 + b2 < c2, the triangle is obtuse.
32B
Tell if the measures can be the side
lengths of a triangle. If so, classify the
triangle as acute, obtuse, or right.
3.8, 4.1, 5.2
a2
+
3.82
b2
+
?
= c2
?
2
4.1 =
5.22
?
14.44 + 16.81= 27.04
31.25 > 27.04
Since a2 + b2 > c2, the triangle is acute.
32C
Tell if the measures can be the side
lengths of a triangle. If so, classify the
triangle as acute, obtuse, or right.
4, 3, 5
a2
42
+
+
b2
?
2
3 =
?
= c2
52
?
16 + 9= 25
25 = 25
Since a2 + b2 = c2, the triangle is right.
33A Find x.
33B
Find x
Rationalize the denominator.
33C
Find the values of x and y.
Leave your answer in simplest
radical form.
22 = 2x
Hypotenuse = 2(shorter leg)
11 = x
Divide both sides by 2.
Substitute 11 for x.
34A
A polygon with 8 sides is
called a(n):
a. Pentagon
b. Quadrilateral
c. Octagon
d. Heptagon
C. Octagon
34B
What is the name of this
polygon.
Pentagon
34C
A polygon with 10 sides is
called a _________________.
Decagon
35A
Find the sum of the interior
angle measures of a
convex heptagon.
(n – 2)180°
Polygon  Sum Thm.
(7 – 2)180°
A heptagon has 7 sides, so
substitute 7 for n.
900°
Simplify.
35B
Find the measure of each
interior angle of a regular
decagon.
(n – 2)180°
Polygon  Sum Thm.
(10 – 2)180° = 1440°
Substitute 10 for n and
simplify.
The int. s are , so divide by 10.
35C
Find the measure of each
exterior angle of a regular
20-gon.
measure of one ext.  =
36A
Which is NOT property of all
parallelograms
a. Two pairs of parallel opposite
sides.
b. One pair of parallel and
congruent opposite sides
c.
Two pairs of congruent
opposite sides
d. Four congruent angles
D. Four Congruent Angles
36B
A quadrilateral with four
congruent sides AND four
congruent angles is called
a(n) _____________.
Square
36C
If a quadrilateral has one pair
of opposite sides are parallel
but NO right angles. Which
shape could it be?
a. Rhombus, square
b. Square, trapezoid
c. Rectangle, quadrilateral
d. Quadrilateral, trapezoid
D. Quadrilateral, Trapezoid
37A
A parallelogram with 4
congruent sides, but the
angles are not congruent is
a(n):
a. Rhombus
b. Rectangle
c. Trapezoid
d. Square
A. Rhombus
37B
A parallelogram with 4
congruent sides and 4
congruent angles is a(n):
a. Rhombus
b. Rectangle
c. Trapezoid
d. Square
D. Square
37C
A square might also be called.
I.
Rectangle
II.
Rhombus
III. Parallelogram
a. I and II only
c. II and III
b. I and III only
d. I, II, and III
D. I, II, and III
38A
In kite ABCD, mDAB =
54°, and mCDF = 52°.
Find mBCD.
mBCD + mCBF + mCDF = 180°
mBCD + mCBF + mCDF = 180°
mBCD + 52° + 52° = 180°
mBCD = 76°
38B
Find mA.
mC + mB = 180°
100 + mB = 180
Same-Side Int. s Thm.
Substitute 100 for mC.
mB = 80°
A  B
Subtract 100 from both sides.
Isos. trap. s base 
mA = mB
Def. of  s
mA = 80°
Substitute 80 for mB
38C
JN = 10.6, and NL = 14.8.
Find KM.
KM = JN + NL
KM = 10.6 + 14.8 = 25.4
39A
Sole the proportion.
7(72) = x(56)
504 = 56x
x=9
Cross Products Property
Simplify.
Divide both sides by 56.
39B
Solve the proportion.
2y(4y) = 9(8)
8y2 = 72
Cross Products Property
Simplify.
y2 = 9
Divide both sides by 8.
y = 3
Find the square root of both sides.
y = 3 or y = –3
Rewrite as two equations.
39C
Marta is making a scale drawing of her
bedroom. Her rectangular room is 12.5
feet wide and 15 feet long. On the scale
drawing, the width of her room is 5
inches. What is the length?
5(15) = x(12.5)
75 = 12.5x
x=6
Cross Products Property
Simplify.
Divide both sides by 12.5.
40A
Determine whether the polygons are similar. If
so, write the similarity ratio and a similarity
statement.
rectangles ABCD and EFGH
A  E, B  F,
C  G, and D  H.
All s of a rect. are rt. s
and are .
Thus the similarity ratio is , and rect. ABCD ~ rect. EFGH.
40B
Determine whether the polygons
are similar. If so, write the similarity
ratio and a similarity statement.
Since no pairs of angles
are congruent, the triangles
are not similar.
40C
Find the length of the
model to the nearest tenth
of a centimeter.
5(6.3) = x(1.8)
Cross Products Prop.
31.5 = 1.8x
Simplify.
17.5 = x
Divide both sides by 1.8.
41A
Explain why the triangles
are similar and write a
similarity statement.
mC = 47°, so C  F. B  E
Therefore, ∆ABC
~ ∆DEF by AA ~.
41B
Are the triangles similar. If so
name the postulate or
theorem.
Therefore ∆PQR ~ ∆STU by SSS ~.
41C
Are the triangles similar. If so
name the postulate or
theorem.
TXU  VXW by the
Vertical Angles Theorem.
Therefore ∆TXU ~ ∆VXW by SAS ~.
42A
Find US
Substitute 14 for RU,
4 for VT, and 10 for RV.
US(10) = 56
Cross Products Prop.
Divide both sides by 10.
42B
Find PN
Substitute in the given values.
2PN = 15
PN = 7.5
Cross Products Prop.
Divide both sides by 2.
42C
Find PS and SR
Substitute the given values.
40(x – 2) = 32(x + 5)
Cross Products Property
40x – 80 = 32x + 160 Distributive Property
x = 30
PS = x – 2 = 28
SR = x + 5 = 35
43A
Tyler wants to find the height of a
telephone pole. He measured the pole’s
shadow and his own shadow and then
made a diagram. What is the height h of
the pole?
Step 1 Convert the
measurements to inches.
AB = 7 ft 8 in. = (7  12) in.
+ 8 in. = 92 in.
BC = 5 ft 9 in. = (5  12) in.
+ 9 in. = 69 in.
FG = 38 ft 4 in. = (38  12) in.
+ 4 in. = 460 in.
92h = 69  460 The height h of the
pole is 345 inches,
h = 345
or 28 feet 9 inches.
43B
The rectangular central chamber of the
Lincoln Memorial is 74 ft long and 60 ft
wide. Make a scale drawing of the floor of
the chamber using a scale of 1 in.:20 ft.
Find the length and width of the scale
drawing.
20w = 60
w = 3 in
3.7 in.
3 in.
43C
Maria is 4 ft 2 in. tall. To find the height of a
flagpole, she measured her shadow and the
pole’s shadow. What is the height h of the
flagpole?
25 ft
44A
Write the trigonometric ratio as a fraction
and as a decimal rounded to the nearest
hundredth.
sin J
44B
Write the trigonometric ratio as a
fraction and as a decimal rounded
to the nearest hundredth.
tan K
44C
Find the measure of angle D
5.3
0
tan D 
 68
2. 1
1
45A
Find BC.
Write a trigonometric ratio.
Substitute the given values.
Multiply both sides by BC
and divide by tan 15°.
BC  38.07 ft
Simplify the expression.
45B
Find the length of QR
Substitute the given values.
12.9(sin 63°) = QR
11.49 cm  QR
Multiply both sides by 12.9.
Simplify the expression.
45C
Find the length of FD
Substitute the given values.
Multiply both sides by FD and
divide by cos 39°.
FD  25.74 m
Simplify the expression.
46A
The Seattle Space Needle casts a 67meter shadow. If the angle of
elevation from the tip of the shadow
to the top of the Space Needle is
70º, how tall is the Space Needle?
Round to the nearest meter.
You are given the side adjacent to
A, and y is the side opposite A.
So write a tangent ratio.
y = 67 tan 70° Multiply both sides by 67.
y  184 m
Simplify the expression.
46B
Use the diagram above to classify
each angle as an angle of elevation
or angle of depression.
1a. 5
1b. 6
1a. Depression
1b. Elevation
46C
A plane is flying at an altitude of 14,500
ft. The angle of elevation from the control
tower to the plane is 15°. What is the
horizontal distance from the plane to the
tower? Round to the nearest foot.
14500
tan 15 
x
54,115 ft
47A
Given the figure, segment JM
is best described as:
a. Chord
b. Secant
c. Tangent
d. Diameter
A. Chord
47B
Given the figure, Line JM is
best described as:
a. Chord
b. Secant
c. Tangent
d. Diameter
B. Secant
47C
Given the figure, line m is
best described as:
a. Chord
b. Secant
c. Tangent
d. Diameter
C. Tangent
48A
Find a.
5a – 32 = 4 + 2a
3a – 32 = 4
3a = 36
a = 12
48B
Find RS
n + 3 = 2n – 1
4=n
RS = 4 + 3
=7
48C
Find RS
x = 4x – 25.2
–3x = –25.2
x = 8.4
= 2.1
49A
Find
mLJN
mLJN = 360° – (40 +
25)°
= 295°
49B
Find n.
9n – 11 = 7n + 11
2n = 22
n = 11
49C C  J, and mGCD  mNJM.
Find NM.
14t – 26 = 5t + 1
9t = 27
t=3
NM = 5(3) + 1
= 16
50A
Find each measure.
mPRU
50B
Find each measure.
mSP
50C
Find each measure.
mDAE
51A
Find each measure.
mEFH
= 65°
51B
Find each measure.
51C
Find each angle measure.
mABD
52A
Find the value of x.
50° = 83° – x
x = 33°
52B
Find the value of x.
EJ  JF = GJ  JH
10(7) = 14(x)
70 = 14x
5=x
J
52C
Find the value of x.
ML  JL = KL2
20(5) = x2
100 = x2
±10 = x
53A
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53B
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53C
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54A
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54B
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54C
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55A
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55B
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56A
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56B
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57A
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58A
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59A
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60A
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61A
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62A
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63A
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64A
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64C
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