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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 don’t 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.
x
K
L
M
2.5x
_____________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
________________________
2
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.
(2x + 5)°
1
2
(4x -5)°
7) What is the angle measure of <1 & < 2?
8) Find the area of the polygon.
12 ft
5ft
9ft
15ft
A = ______________
9) If <A and <B are supplementary angles and m< A = ½ m<B, find m<A and m<B.
m<A = ___________
m< B = ___________
3
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 degrees,” write the converse.
Chapter 3: Parallel and Perpendicular Lines
12) Name all the segments that are parallel to
BC
E
F
D
13) Name all segments that are perpendicular to
C
BC
14) Name a pair of skew lines.
H
A
15) Name a pair of parallel planes.
1
3
G
B
2
m
4
5 6
7 8
mn
n
Use the diagram above for questions # 16 -25
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.
19) Name all pairs of alternate interior angles.
22) Name all angles that are supplementary
to < 1.
23) Line k is a transversal line of m and n. Name a pair of angles whose equality would guarantee that line m is parallel to line q.
4
Then find the angle measures. Use the diagram above.
24) m<4 = (8x – 34 )°; m<5 = (5x + 2)°
m < 4 = ____________
m <5 = ___________
25) m<1 = (23x + 11)°; m<7 = (14x + 21)°
m< 1 = ____________
m < 7 = ____________
Chapter 4: Triangle Congruencies
26) 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
D
C
ADC  ABC
A
c.
Prove
B
ABC  DEC
A
A
D
A
B
d. Prove ABC ADEC
E
A
C
A
A
B
C
E
D
5
27) Find the measure of each angle.
(2x+19)º
3x°
(x+5)°
28) Find the measure of x.
(2x + 3)°
(4x – 7)°
29) Determine which of the following side lengths are possible measures for the side lengths of a triangle.
a. 1, 1, 4
b. 2, 9, 11
c. 4, 5, 7
d. 6, 6, 12
e. 5, 9, 13
Chapter 5: Properties and Attributes of Triangles
30) Find the measure of <R and <P.
m<R:_____________
P
R
(2x-10)º
31) Find the value of x.
(x)º
(4x -34)º
Q
m<P:_____________
6
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) Given L is the centroid of triangle WFD, if RL = 8 mm, find LD.
W
R
L
F
J
Q
D
35) Is AB an altitude, median, angle bisector, perpendicular bisector, or none?
More than one answer may apply.
45°
Find the missing sides below; answers must be expressed in radical form only.
45°
2 6
45°
b
a
b
16
a
45°
a
45°
45°
7
b
30°
30°
b
30°
a
a
6 5
b
a
60°
60°
60°
4
3
b
7
36) Simplify the expressions, rationalize any denominators.
a)
b)  180
48
c)
96
3
d)
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) Find the value of x.
101° 105°
104°
115°
137°
x
40) Classify the following figure as a parallelogram, a rectangle, rhombus or square. Remember to classify all that apply.
41) Find the length of the midsegment, x.
1
7
8
42) 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
43) PQRS is a rectangle. PQ = 64 ft and PR =70 ft. Find each measure.
a) SR
b) TQ
Chapter 7: Similarity
44) 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?
45) The two rectangles are similar. Find x to the nearest tenth.
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Chapter 8: Right Triangles and Trigonometry
46) 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
47) If PS = 6 and PT = 9, find PR.
48) If TP = 15 and PR = 5, find PS
49) Use the special right triangles to find the following ratios.
a. Sin(60º)
b. Cos (30º)
c. Tan (30º)
d. Tan (45º)
50) Find CB & AC
AC =
CB =
<C=
51) Find the unknown measures and angles. Round the measures to the nearest tenth and the angles to the nearest degree.
DF =
<D =
<F=
52) 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.
10
Chapter 9: Perimeter, Circumference & Area
53) 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
54) If the circumference of a circle is 220 m, find the diameter and round your answer to the nearest tenth.
55) Find the area of circle if the circumference is 20π.
Chapter 11: Circles
56) Find the areas of the following sectors, round to the nearest tenth if necessary.
57) Find the areas of the segments below, round to the nearest tenth if necessary.
3
11
58) Find the minor arc lengths below, round to the nearest tenth if necessary.
59) Find each value or measure.
Chapter 10: Spatial Reasoning
60) Find the surface area of the following figures below, round to the nearest tenth if necessary.
8cm
16cm
61) Find the surface area of the following figures below, round to the nearest tenth if necessary.
12
62) Find the volume of the following figures below, round to the nearest tenth if necessary.
63) Find the volume of the following figures below, round to the nearest tenth if necessary.