Geometry Semester Exam Study Guide
Geometry Semester Exam 2015-2016
30 questions
Topics:
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Basic transformations
Parallel lines
Constructions
Coordinate geometry
Slope and equations of a line
Congruency Theorems for triangles
Pythagorean Theorem proof
Similar triangles
Sine, Cosine, Tangent in right triangles
Reporting Category 1: (83% of the Semester Exam)
Congruence, Similarity, Right Triangles and Trigonometry
Reporting Category 2: (17% of the Semester Exam)
Circles, Geometric Measurement, and Geometric Properties
with Equations
 This Study Guide includes sample problems from the textbook that
students can use to help prepare for the exam.
 They are NOT the test items.
 This is geared towards the DISTRICT semester exam.
 There will not be a study guide that is geared towards any state
assessment (End of Year EOC).
 Answers will not be provided by District Office for the Study Guide.
Geometry Semester Exam Study Guide
BENCHMARK
DOK
Skill/Concepts
Example problem or problems to support studying
a. A figure has vertices at J(-2, 3), K(0,3), and L(0,1). After a
transformation, the image of the figure has vertices at J’(2,
1), K’(4, 1), and L’(4, -1). Draw the preimage and image.
Then identify the transformation.
b. Find the coordinates for the image of RST with vertices R(1, 4), S(-1, -1), and T(-5, 1) after the translation (x, y)(x-2, y8).
a.
M
Determine which
transformation was
created
M
Determine the value
of x on a set of
parallel lines cut by a
transversal
Solve the following proof for Triangle Sum Theorem.
MAFS.912.G-CO.3.10
M
Determine statement
necessary for proving
the sum of interior
angles of a triangle
proof
M
Determine steps in
constructing
perpendicular lines
a. Construct a line perpendicular to line p. State your steps.
MAFS.912.G-CO.4.12
MAFS.912.G-CO.2.6
L
Determine which
transformation will
not create a
congruent figure
MAFS.912.G-GPE.2.4
M
Determine the third
coordinate for an
isosceles triangle
MAFS.912.G-GPE.2.5
M
Determine the slope
of a line segment of a
triangle
MAFS.912.G-CO.4.12
M
Determine steps in
constructing an angle
bisector
MAFS.912.G-CO.1.5
MAFS.912.G-CO.3.9
b.
a. Determine whether triangle ABC is congruent with triangle
PQR using transformations as reasons. A(1, 1), B(4, 1), C(4, 3)
P(-4, 2), Q(-1, 2), R(-1, 4)
b. Prove that the triangles with the given vertices are
congruent. A(3, 1), B(2, -1), C(7, -1) and P(-3, -2) Q(-5, -1),
R(-5, -6)
a. Triangle FGH is isosceles. The vertices for F and G are (1, -1)
and (3, 5) respectively. What is the coordinate for H?
b. Trinagle PQR is isosceles. The vertices for P and Q are (4, 0)
and (-3, 3) respectively. What is the coordinate for R?
a. Triangle ABC is a right triangle on an xy-coordinate plane.
Line segment AC is the hypotenuse of triangle ABC. Vertex A
is at (-4, -3) and Vertex B is at (5, 1). What is the slope of line
segment BC?
b. Triangle PQR is a right triangle on an xy-coordinate plane.
Line segment PR is the hypotenuse of triangle PQR. Vertex P
is at 3, 4) and Vertex Q is at (6, 10). What is the slope of line
segment QR?
a. Construct an angle bisector. State your steps.
Geometry Semester Exam Study Guide
MAFS.912.G-CO.2.7
L
Determine angle
measure of
congruent triangles
State which postulate, if any, can be used to prove the triangles
congruent.
MAFS.912.G-CO.2.8
MAFS.912.G-CO.3.10
M
Determine which
triangle congruency
theorem is necessary
to prove triangles are
congruent
H
Determine the
missing statement of
a triangle proof
a.
MAFS.912.G-SRT.1.2
M
Determine the
missing length in a
similar triangle
b.
a. Given triangle ABC is a right triangle with altitude CD, prove
ABC ~ ACD ~CBD.
MAFS.912.G-SRT.2.4
L
Determine the step
in a proof of the
Pythagorean
Theorem
b. Write a similarity statement that compares the three
triangles below.
Geometry Semester Exam Study Guide
a. Which statement, if true, would be sufficient to demonstrate
that EF is parallel to BC?
MAFS.912.G-SRT.2.4
M
Determine what
statement is
necessary to proof
lines are parallel in a
triangle
b. A student states UV must be parallel to ST. Do you agree
why or why not?
a. To find the width of a river, Jordan surveys the area and
finds the following measures. Find the width of the river.
MAFS.912.G-SRT.2.5
M
Determine the
missing dimension in
similar triangles
b. To calculate the length of a marsh, a surveyor produced the
following diagram. Find the length of the marsh to the
nearest tenth of a unit.
a. Name a ratio that is equivalent to sin P.
MAFS.912.G-SRT.3.6
M
Determine an
equivalent sine ratio
sin 𝐴
MAFS.912.G-SRT.3.7
MAFS.912.G-SRT.3.8
M
Determine the
relationship between
sine and cosine
M
Solve for x using
Pythagorean
Theorem
a. What is cos 𝐵?
a. A tent is supported by a guy rope tied to a stake, as shown in
the diagram. What is the length of the rope?
Geometry Semester Exam Study Guide
b. Stephanie is planning a right triangular garden. She marked
two sides that measure 24 feet and 25 feet. What is the
length of side n?
a.
MAFS.912.G-CO.2.8
H
Determine the
missing reason from
a triangle congruency
proof
MAFS.912.G-GPE.2.4
M
Find the coordinates
of a point that meet
a given ratio that
partitions the
segment
MAFS.912.G-SRT.1.2
M
Determine what the
relevance of dilations
to similarity
M
Determine the type
of triangle given
three coordinates
MAFS.912.G-SRT.1.3
L
Determine which
statement is true
when given AA
criteria
MAFS.912.G-GPE.2.5
M
Determine the
equation of a line
perpendicular to a
MAFS.912.G-SRT.1.2
b.
a. Find the coordinates of the point P that lies along the
directed line segment from A(3, 4) to B(6, 10) and partitions
the segment in the ratio 3 to 2.
b. Find the coordinates of the point P that lies along the
directed segment from J(-2, 5) to K(2, -3) and partitions the
segment in the ratio 4 to 1.
a. Given A(0, 0), B(-1, 1), C(3, 2), D(-2, 2), and E(6, 4).
Prove: ABC~ADE
a. The vertices of triangle RST are R(3, 2), S(-2, 3), and T(-2, 1).
What type of triangle is RST?
b. The vertices of triangle LMN are L(-2, -2), M(1, 3), and N(3,
0). What type of triangle is LMN?
a. Explain why the triangles are similar and write a similarity
statement.
Given the equation of the line and point P not on the line, find
the equation of a line parallel to the given line and a line
perpendicular to the given line through the given point.
Geometry Semester Exam Study Guide
given line with a
given point
MAFS.912.G-SRT.3.6
MAFS.912.G-SRT.3.7
M
M
Determine the
measure of an angle
given two
dimensions
Use the relationship
between sine and
cosine to solve
problems
a. 𝑦 = 3𝑥 + 7; 𝑃(2, 3)
b. 𝑦 = −2𝑥 − 5; 𝑃(−1, 4)
c. 4𝑥 + 3𝑦 = 8; 𝑃(4, −2)
Find each length. Round to the nearest tenth.
Find the side lengths to nearest hundredth and the angle
measure to the nearest degree.
A(2, 0); B(2, -5); C(1, -5)
a. The cosine of a 30 degree angle is equal to the sine of a __
angle.
b. What has the same value as sin M?
Write an equation that can be used to find the unknown angle
measures and unknown measures.
MAFS.912.G-SRT.3.8
M
Determine how to
find the missing
angle
a. In a figure was transformed by dilating the figure and then
reflecting across a line. What must be true?
MAFS.912.G-SRT.1.3
MAFS.912.G-GPE.2.6
L
M
Determine what
criteria must be true
if a triangle is
transformed
Determine the
coordinates of point
of a partitioned line
segment
a. Find the coordinates of the point P that lies along the
directed segment from R(-3, -4) to S(5, 0) and partitions the
segment in the ratio 2 to 3.
b. The map shows a streight highway between two towns.
Highway planners want to build two new rest stops between
the towns so that the two rest stops divide the highway into
Geometry Semester Exam Study Guide
three equal parts. Find the coordinates of the points at
which the rest stops should be built.
MAFS.912.G-GPE.2.7
M
Determine the
perimeter of a
triangle
a. A triangle with vertice P(4, 0), Q(-3,3) and R(4, 6). What is
the perimeter of the triangle?
b. A trinagle has the coordinates J(-1, 0), K(2, 4), and M(7, 1).
What is the perimeter of the triangle to the nearest tenth?