Download Final Review Sheet (Holt Text)(2013)

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Name:
Date:
Geometry Review Sheet for Final
Reviewing for an exam and studying are very important. Take this review packet seriously. The more effort you
put in here, the better you should do on your exam. Remember, ask questions when you do not understand but
make a good effort at the problem first! Use your notes that you have taken throughout the year. Make sure you
read all directions CAREFULLY!!!
Chapter 1: Foundations of Geometry
1) If E is the midpoint of DF , DE = 2x + 4 and EF = 3x – 1. Find DE, EF, and DF.
DE =___________________
EF=____________________
DF=____________________
2) Find the length of LM.
K
x
L
2.5x
M
____________5x – 3 __________________
LM=____________________
3) T is in the interior of <PQR. Find each of the following.
a. mPQT if mPQR= 35º and mRQT =10 º.
________________________
b. mPQR if mPQR= (2x + 35)º, mRQT = (x – 5)º and mPQT = (6x + 10)º
________________________
c. mPQR if QT bisects PQR, mRQT = (3x + 8)º and mPQT = (9x – 4)º
________________________
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4)
DEF and FEG are complementary. mDEF = (5y + 1) º, and mFEG = (3y – 7)º. Find the measure of both
angles.
mDEF=________________
mFEG=________________
5) DEF and FEG are supplementary. mDEF = (3z + 12) º and mFEG = (7z – 32)º. Find the measures of both
angles.
m<DEF=_______________
m<FEG=________________
6) Use your knowledge of vertical angles to solve for x. (Not drawn to scale)
7) What is the angle measure of 1 &  2?
1
2x + 5
8) Find the area of the polygon.
12 ft
4x – 5
2
5ft
9ft
15ft
Area = ____________
9) If A and B are supplementary angles and mA = ½ mB, find mA and mB.
mA = ___________
mB = ___________
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Chapter 2: Geometric Reasoning
10) Write the converse, inverse, and contra positive of the conditional statement “If Stephanie’s birthday is
January 1st, then she was born on New Year’s Day.” Find the truth-value of each.
11) For the conditional “If an angle is straight, then its measure is 180°,” write the converse.
Chapter 3: Parallel and Perpendicular Lines
12) Name all the segments that are parallel to BC
E
F
D
C
13) Name all segments that are perpendicular to BC
H
A
14) Name a pair of skew lines.
15) Name a pair of parallel planes.
G
B
4
1
3
2
m
4
5 6
7 8
mn
n
Use the diagram above for questions # 16 -24
16) Name all pairs of vertical angles.
20) Name all pairs of alternate exterior angles.
17) Name all pairs of same side interior angles
21) Name all pairs of same side exterior angles.
18) Name all pairs of corresponding angles.
22) Name all angles that are supplementary
to  1.
19) Name all pairs of alternate interior angles.
23) Line k is a transversal line of m and n.
24) Name a pair of angles whose equality would guarantee that line m is parallel to line q.
Then find the angle measures. Use the diagram above.
25) m4 = (8x – 34 )°; m5 = (5x + 2)°
m 4 = ____________
m 5 = ____________
26) m1 = (23x + 11)°; m7 = (14x + 21)°
m1 = ____________
m 7 = ____________
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Chapter 4: Triangle Congruencies
27) Label each diagram appropriately and identify which triangle congruence theorem satisfies the diagram. Choose
from SSS, SAS, ASA, AAS, HL or not possible. If it is not possible, explain why. Show all work; put a box
around your answer. Triangles are not drawn to scale.
a. Prove
ABD  ACD
A
B
b. Prove
C
D
ADC  ABC
D
C
A
c. Prove
B
ABC  DEC
A
A
d. Prove
D
A
B
A
ABC  DEC
E
A
C
A
A
B
C
E
D
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28) Find the measure of each angle.
(2x+19)º
(x+5)°
3x°
29) Find the measure of x.
(2x + 3)°
(4x – 7 )°
Chapter 5: Properties and Attributes of Triangles
30) Find the measure of R and P.
P
R
(2x – 10)º
mR:_____________
(4x – 34)º
Q
mP:_____________
31) Find the value of x.
(x)º
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32) Sir Shrek is off to rescue Princess Fiona in the highest tower of the castle. He shoots an arrow with a 75 foot rope
attached to it, to the top of the tower. Shrek is stand 20 feet away from the tower when he shoots the arrow. How
tall is the tower he has to climb in order to rescue Princess Fiona?
33) Find the perimeter of a square with a diagonal 20 cm long.
34) Find the length of line segment CD, if AB = 26; AE = 10 and mC = 45°.
C
B
A
E
F
D
35) Find all missing sides below; answers must be expressed in radical form only.
45°
45°
45°
16
2 6
45°
45°
45°
7
30°
30°
30°
6 5
60°
60°
60°
4
3
8
36) Simplify the expressions, rationalize any denominators.
a)
48
b)  180
c)
96
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Chapter 6: Polygons & Quadrilaterals
37) Find the measure of each interior angle of a regular 15-gon.
38) Find the sum of the interior angle measures of a regular 15-gon.
39) Quadrilateral PQRS is a parallelogram. PT = 53, PS = 76, and mQRS = 75º.
Find each measure.
A.) RT
B.) QR
C.) mRQP
D.) mRSP
E.) mQPS
F.) RS
40) PQRS is a rectangle. PQ = 64 ft and PR =70 ft. Find each measure.
a) SR
b) TQ
d)
1
7
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41) Identify as sometimes, always or never
i. A parallelogram is a rhombus.
ii. A rhombus is a square.
iii. A rhombus is a rectangle.
_____________
_____________
_____________
Chapter 7: Similarity
42) A rectangle is 3.2 centimeters wide and 8 centimeters long. A similar rectangle is 5 centimeters long, what is the
width of the second rectangle?
43) The two rectangles are similar. Find x to the nearest tenth.
44) Determine the following.
Chapter 8: Right Triangles and Trigonometry
45) Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.
a. 8 and 18
b. 6 and 15
46) If PS = 6 and PT = 9, find PR.
47) If TP = 15 and PR = 5, find PS
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48) Use the special right triangles to find the following ratios.
a. Sin(60º)
b. Cos (30º)
c. Tan (30º)
d. Tan (45º)
49) Find CB & AC
AC =
CB =
mC=
50) Find the unknown measures and angles. Round the measures to the nearest tenth and the angles to the nearest
degree.
DF =
mD =
mF=
51) A plane is flying at an altitude of 14,500 ft. The angle of depression from the plane to a control tower is 15°. What
is the horizontal distance from the plane to the tower? Round to the nearest foot.
Chapter 9: Perimeter, Circumference & Area
52) Find the areas of the shaded regions below. Round to the nearest tenth if necessary.
4
3
9
3
4
3
3
4
9
2
9
9
4
3
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Chapter 11: Circles
53) Find the areas of the following sectors, round to the nearest tenth if necessary.
54) Find the areas of the segments below, round to the nearest tenth if necessary.
55) Find the arc lengths below, round to the nearest tenth if necessary.
56) Find each value or measure.
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Chapter 10: Spatial Reasoning
57) Find the surface area of the following figures below, round to the nearest tenth if necessary.
8cm
16cm
58) Find the surface area of the following figures below, round to the nearest tenth if necessary.
59) Find the volume of the following figures below, round to the nearest tenth if necessary.
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60) Find the volume of the following figures below, round to the nearest tenth if necessary.