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Geometry Semester Exam Study Guide
MS/HS Geometry Semester Exam
30 questions
Unit 1 Standards: (4 Questions)
“Points, Lines, Angles and Shapes”
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Know precise definitions of angle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line,
and distance along a line. – MAFS.912.G-CO.1.1
Prove theorems about lines and angles (Including vertical angles are congruent; when a transversal crosses parallel lines, alternate
interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are
exactly those equidistant from the segment’s endpoints.) – MAFS.912.G-CO.3.9
Prove theorems about triangles (Including measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base
angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and
half the length; the medians of a triangle meet at a point.) - MAFS.912.G-CO.3.10
Make a construction (Including copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing
perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a
point not on the line.) – MAFS.912.G-CO.4.12
MAFS.912.G-CO.1.1
“A pair of perpendicular lines are two lines that intersect at exactly one point. What is not precise about this definition?
MAFS.912.G-CO.3.9
Prove ∠1 ≅ ∠8.
Geometry Semester Exam Study Guide
MAFS.912.G-CO.3.10
What additional information is required in order to prove the two triangles are congruent using the provided justification?
Use the set of choices in the box below. Select a side or angle and place it in the appropriate region. Only one side or angle can be placed in
each region.
MAFS.912.G-CO.4.12
You have been asked to place a warehouse so that it is an equal distance from the three roads indicated on the following map. Find this
location and show your work.
Show how to fold your paper to physically construct this point as an intersection of two creases. Explain why the above construction works
and, in particular, why you only needed to make two creases.
Unit 2 Standards: (6 Questions)
“Coordinate Geometry”
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Know precise definitions of angle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line,
and distance along a line. – MAFS.912.G-CO.1.1 (2 questions)
Use coordinates to prove simple geometric theorems algebraically (For example, students could be asked to determine whether
points listed are a square or to find the last point to create a right triangle, given the first two.) – MAFS.912.G-GPE.2.4 (2 questions)
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Geometry Semester Exam Study Guide
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a
line parallel or perpendicular to a given line that passes through a given point). - MAFS.912.G-GPE.2.5 (2 questions)
MAFS.912.G-CO.1.1
What is the definition of a line segment?
MAFS.912.G-GPE.2.4
���� has endpoint B at (24, 16). The midpoint of 𝐴𝐵
���� is P(4, -3). What is the y-coordinate of Point A?
a. On a coordinate grid, 𝐴𝐵
b. Prove or disprove that triangle ABC with coordinates A(-1, 2), B(1, 5), C(-2, 7) is an isosceles right triangle.
MAFS.912.G-GPE.2.5
a. Verify that the distance between two parallel lines is constant.
Justify your answer.
Unit 3 Standards: (8 Questions)
“Congruent and Similar Triangles”
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Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. (Theorems could be SS-S, A-S-A, Hypotenuse-Leg, or S-A-S) – MAFS.912.G-CO.2.6
Show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. MAFS.912.G-CO.2.7
Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in
terms of rigid motions. - MAFS.912.G-CO.2.8
Prove theorems about triangles (Including measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base
angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and
half the length; the medians of a triangle meet at a point.) - MAFS.912.G-CO.3.10
Explain the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all
corresponding pairs of sides. - MAFS.912.G-SRT.1.2
Prove theorems about triangles. (Theorems including: a line parallel to one side of a triangle divides the other two proportionally,
and conversely; the Pythagorean Theorem proved using triangle similarity.) - MAFS.912.G-SRT.2.4 (2 questions)
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. - MAFS.912.GSRT.2.5
Geometry Semester Exam Study Guide
MAFS.912.G-CO.2.6/ MAFS.912.G-CO.2.7/ MAFS.912.G-CO.2.8 *Transformations will NOT be covered on the semester exam, just the
similarity and congruency piece within each of these standards.
Consider a ∆𝐴𝐵𝐶 that has been transformed through rigid motions and its image is compared to ∆𝑋𝑌𝑍. Determine if the given information
is sufficient to draw the provided conclusion.
MAFS.912.G-CO.3.10
*See question type from Unit 1.
MAFS.912.G-SRT.1.2
In the picture below, line segments AD and BC intersects at X. Line segments AB and CD are drawn, forming two triangles, AXB and CXD.
In items a-d below, some additional assumptions about the picture are given. In each problem, determine whether the given assumptions
are enough to prove that the two triangles are similar.
a. The lengths AX and XD satisfy the equation 2AX = 3XD.
𝐴𝑋
𝐷𝑋
b. The lengths AS, BX, CX, and DX satisfy the equation 𝐵𝑋 = 𝐶𝑋 .
c. Lines AB and CD are parallel.
Angle XAB is congruent to angle XCD.
Geometry Semester Exam Study Guide
MAFS.912.G-SRT.2.4
Use the figure below to answer questions a-c.
a. Is 𝑎2 = 𝑐𝑑? How do you know?
b. Is 𝑎2 + 𝑏 2 = 𝑐𝑑 + 𝑐𝑒? How do you know?
c. Is 𝑐 = 𝑑 + 𝑒? How do you know?
MAFS.912.G-SRT.2.5
Pablo is practicing bank shots on a standard 4 ft.-by-8 ft. pool table that has a wall on each side, a pocket in each corners and a pocket at
the midpoint of each 8-ft. side.
Pablo places the cue ball one foot away from the south wall of the table and one foot away from the west wall, as shown in the diagram
below. He wants to bank the cue ball off of the east wall and into the pocket at the midpoint of the north wall.
At what point should the cue ball hit the east wall?
Geometry Semester Exam Study Guide
Unit 4 Standards: (6 Questions)
“Right Triangles and Trigonometric Ratios”
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Definitions of trigonometric ratios for acute angles within right triangles (Calculating angles using trigonometric ratios) –
MAFS.912.G-SRT.3.6 (2 questions)
• Explain and use the relationship between sine and cosine of complimentary angles. – MAFS.912.G-SRT.3.7 (2 questions)
• Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems. - MAFS.912.G-SRT.3.8 (2 questions)
MAFS.912.G-SRT.3.6
The figure below shows two right angles. The length of AE is x units and the length of DE is 40 units.
Using the triangle above, find the following:
a. 𝑥 =
b. sin A =
c. cos 𝐴 =
d. tan 𝐴 =
MAFS.912.G-SRT.3.7
a. Find the second acute angle of a right triangle given that the first acute angle has measure of 39°.
b. Complete the following statement: If sin 300° = ½, then the cos ____ = ½.
c. Find: sin A, sin B, cos A, cosB from the triangle below
MAFS.912.G-SRT.3.8
a. A teenager whose eyes are 5’ above ground level is looking into a mirror on the ground and can see the top of a building that is 30’
away from the teenager. The angle of elevation from the center of the mirror to the top of the building is 75°. How tall is the
building? How far away from the teenager’s feet is the mirror?
Unit 5 Standards: (6 Questions)
“Quadrilaterals”
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Geometry Semester Exam Study Guide
Prove theorems about parallelograms; use theorems about parallelograms to solve problems. (Theorems including opposite sides
are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.) - MAFS.912.G-CO.3.11 (2 questions)
Find the point on a directed line segment between two given points that partitions the segment in a given ratio. - MAFS.912.GGPE.2.6 (2 questions)
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. MAFS.912.G-GPE.2.7 (2 questions)
MAFS.912.G-CO.3.11
a. Use the quadrilateral ABCD to answer each part. ABCD is a quadrilateral with AB∥CD and AD∥BC, and the diagonals AC and BD
intersect at point E.
∆CBE≅∆ABE
∆ADE≅∆ABE
∆CDE≅∆ABE
True or False
True or False
True or False
MAFS.912.G-GPE.2.6
a. Given A (3, 2) and B (6, 11), find the point that divides the line segment AB two-thirds of the way from A to B. Find the midpoint of
the line segment AB.
b. A point B(4,2) on a segment with endpoints A(2, -1) and C(x,y) partitions the segment in a 1:3 ratio. Find x and y.
Geometry Semester Exam Study Guide
MAFS.912.G-GPE.2.7
a. Find the perimeter and area of a rectangle with vertices at C (-1, 1), D (3, 4), E (6, 0), F (2, -3). Round your answer to the nearest
hundredth when necessary.
b. Find the perimeter of the triangle ABC. Each unit represents 1 cm.