Final Exam Review Packet & Topics List
Geometry 2015
Geometry Final Exam Review Packet
Relationships within Triangles (Bisectors, Medians, Altitudes) (Ch 5)
 Identify and use properties of perpendicular bisectors, angle bisectors in triangles
 Identify and use properties of medians and altitudes in triangles
 Find possible triangle side lengths using Triangle Inequality Theorem (sum of the lengths of
two sides of a triangle is greater than the length of the third side)
Polygons and Quadrilaterals (Ch 6)
 Find the sum of the measures of the interior and exterior angles of a polygon
 Classify and apply properties of parallelogram, rhombus, square, rectangle, trapezoid and
kite in problems
 Classify and Prove a quadrilateral is a parallelogram, rhombus, square, rectangle, trapezoid
or kite given a diagram or given numerical coordinates
Similarity (Ch 7)
 Write ratios and solve proportions
 Determine whether polygons are similar and write similarity statements
 Use AA~ Postulate, and the SAS~ and SSS~ Theorems to prove similar triangles
 Use similarity to find indirect measurements
Right Triangles & Trigonometry (Ch 8)
 Use the Pythagorean Theorem and its converse
 Use the properties of 45-45-90 and 30-60-90 triangles
 Use the sine, cosine and tangent ratios (SOHCAHTOA) to determine side lengths and angles
measurements in right triangles
 Use angles of elevation and depression to solve problems
 Apply the Law of Sines and Cosines
Area (Ch 10)
 Find the area of parallelograms, triangles, trapezoids, rhombuses and kites
 Find the area of regular polygons (using special right triangle rules and SOHCAHTOA)
 Find circumference and arc length of circles
 Find the areas of circles
Volume (Ch 11)
 Find the volume of a prism, cylinder, pyramid, cone and sphere
 Model real-world situations and solve problems using formulas
Circles (Ch 12)
 Use properties of a tangent to a circle
 Use congruent chords, arcs and central angles
 Use perpendicular bisectors to chords
 Find the measure of an inscribed angle
 Find the measure of an angle formed by a tangent and a chord
 Find measures of angles formed by chords, secants, and tangents
 Find the center and radius of a circle
In addition to the included practice problems, it is suggested/recommended that you
review the above topics list and complete the problems in the Chapter Review section
at the end of each chapter listed above. The solutions are in the back of the book to
check your work.
Final Exam Review Packet & Topics List
Geometry 2015
Practice Problems:
Chapter 6 Polygons
Polygon Angle Sum (n-2)180˚
(#1-5) Find the variable and all angle measures.
2.
1.
3.
4.
5.
Interior and Exterior Angles in Polygons
Find the values of the variables for each regular polygon. Round to the nearest
tenth if necessary.
6.
7.
Note: A Regular Polygon has congruent interior angles and congruent sides!
8.
Final Exam Review Packet & Topics List
Geometry 2015
Angles in Parallelograms
Find the value of x in each parallelogram.
9.
10.
11.
12.
13.
14.
Find the measures of the numbered angles for each parallelogram.
15.
16.
17.
18.
Final Exam Review Packet & Topics List
Geometry 2015
For what values of x and y must each figure be a parallelogram?
19.
20.
21.
22.
(#23- 27) Decide whether the parallelogram is a rhombus, a rectangle, or a
square. Explain.
23.
24.
26.
25.
27.
(#28- 31) Find the measures of the numbered angles in each rhombus.
28.
29.
30.
31.
7.
Final Exam Review Packet & Topics List
2015
Geometry
HIJK is a rectangle. Find the value of x and the length of each diagonal.
Draw the rectangle first and then label all parts.
32. HJ = x and IK = 2x 7
34. HJ = 3x + 7 and IK = 6x  11
33. HJ = 3x + 5 and IK = 5x 9
35. HJ = 19 + 2x and IK = 3x + 22
Determine the most precise name for each quadrilateral.
36.
38.
37.
39.
For Exercises 40–43, determine whether the parallelogram is a rhombus, a
rectangle, or a square. Give the most precise description in each case.
40. A parallelogram has perpendicular diagonals and angle measures of 45, 135, 45, and 135.
41. A parallelogram has perpendicular and congruent diagonals.
42. A parallelogram has perpendicular diagonals and angle measures that are all 90.
43. A parallelogram has congruent diagonals.
44. The measures of two complementary angles are in the ratio 2 : 3. What is the
measure of the smaller angle?
45. The measures of two supplementary angles are in the ratio 4 : 11. What is the
measure of the larger angle?
Final Exam Review Packet & Topics List
2015
Chapter 7 Similarity
List the pairs of congruent angles and the extended proportion that relates the
corresponding sides for the similar polygons.
46. ABCD ~ WXYZ
47. MNO ~ RST
Determine whether the polygons are similar. If so, write a similarity statement
and give the scale factor. If not, explain.
48.
49.
Find the value of y. Give the scale factor of the polygons.
50. ABCD ~ TSVU
Geometry
Final Exam Review Packet & Topics List
2015
Geometry
(#51 – #53) Determine whether the triangles are similar. If so, write a similarity statement and
name the postulate or theorem you used. If not, explain
51.
58
52.
53.
Chapter 8 Right Triangles and Trigonometry
Pythagorean Theorem - Find the value of y. Express in simplest radical form.
54.
55.
56.
57.
The lengths of the sides of a triangle are given. Classify each triangle as acute,
right, or obtuse.
58.
3, 8, 10
59.
60. 12, 15, 19
4, 5, 7
Special Right Triangles - Find the value of each variable. If your answer is not an integer,
express it in simplest radical form.
61.
62.
Final Exam Review Packet & Topics List
2015
Geometry
63.
64.
65.
66.
Find the value of each variable. If your answer is not an integer, express it in
simplest radical form.
67.
68.
Write the ratios for sin X, cos X, and tan X.
69.
Find the value of x. Round to the nearest tenth.
70.
72.
71.
73.
Final Exam Review Packet & Topics List
2015
Geometry
Find the value of x. Round to the nearest degree.
74.
75.
77.
76.
Find the value of x. Round to the nearest tenth of a unit.
78.
79.
80.
81.
82. An airplane is flying at an altitude of 10,000 ft. The airport at which it is
scheduled to land is 50 mi away. Find the average angle at which the airplane
must descend for landing. Round your answer to the nearest degree.
83. A lake measures 600 ft across. A lodge stands on one shore. From your point
on the opposite shore, the angle of elevation to the top of the lodge is 4°.
How high above the lake does the lodge stand? Round your answer to the
nearest foot.
Final Exam Review Packet & Topics List
2015
Law of Sines - Use the information given to solve.
82. In ΔABC, mA = 40, mC = 70, and BC = 8.5. To the nearest tenth,
what is AB?
83. In ΔGHK, mG = 105, mK = 32, and GH = 10.2. To the nearest tenth,
what is GK?
84. In ΔXYZ, mY = 76, XY = 15, and XZ = 19. To the nearest tenth,
what is mZ?
85. In ΔABC, mB = 93, AC = 15, and BC = 10. To the nearest tenth,
what is mA?
Law of Cosines - Use the information given to solve.
86. In ΔABC, mA = 40, AB = 9.2, and AC = 8.5. To the nearest tenth,
what is BC?
87. In ΔPQR, mQ = 112, PQ = 12.5, and QR = 14.2. To the nearest tenth,
what is the length of PR ?
88. In ΔGHK, GH = 11, HK = 21, and GK = 15. To the nearest tenth,
what is mK?
Geometry
Final Exam Review Packet & Topics List
2015
Geometry
Ch 12 Circles and Arcs
Name the following in
G.
89. the minor arcs
90. the major arcs
91. the semicircles
Find the length of each darkened arc. Leave your answer in terms of π.
92.
93.
Find each indicated measure for
94. mEYD
Y.
95.
96.
Tangent Lines
97.
is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to
the nearest tenth if necessary.
B
A
r
O
98.
and
are all tangent to O. JA = 9, AL = 10, and CK = 14.
Find the perimeter of
.
J
A
B
O
L
K
C
Final Exam Review Packet & Topics List
2015
Geometry
99. Assume that lines that appear to be tangent to circle O are tangent.
Find the value of x, if
110.
x°
O
Find the measure of each angle or chord length.
100.
101.
102.
103.
Ch 10 Areas of Regular Polygons
Find the area of each regular polygon. Round your answer to the nearest tenth.
104.
105.
106.
Find the area of each parallelogram, triangle, trapezoid, kite, and rhombus.
107.
108.
Final Exam Review Packet & Topics List
2015
Geometry
109.
110.
111.
112.
113.
114.
Chapter 12 Volume
Find the volume of each solid.
115.
116.
117.
118.
Final Exam Review Packet & Topics List
2015
Geometry
Chapter 5 Bisectors, Altitudes and Medians in Triangles
Is AB a median, an altitude, a perpendicular bisector, or none of these? How do you know?
119.
120.
121.
Can a triangle have sides with the given lengths? Explain.
122. 2 in., 3 in., 5 in.
123. 9 cm, 11 cm, 15 cm
List the sides of each triangle in order from shortest to longest.
124.
125.