Download D. bisector of an angle 2. If T is the midpoint of and V lies between R

D.
bisector of an angle
2. If T is the midpoint of
and V lies between R and T, which statement must be true?
MACC.912.G-CO.3.9
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A.
B.
C.
D.
3. Duplicating an angle can be accomplished using a compass and a straightedge. An example of duplicating
Angle PQR is shown below.
How many of the construction marks were made using a compass?
MACC.912.G-CO.4.12
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A.
2
B.
3
C.
4
D.
5
4. What is being constructed in the figure?
MACC.912.G-CO.4.12
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A.
B.
C.
D.
5. An angle is a geometric figure that consists of
MACC.912.G-CO.1.1
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A.
two intersecting lines.
B.
a number between 0 and 360.
C.
two rays with a common endpoint.
D.
two distinct points and all the points between them.
6. A team of students created the following diagram based upon given information.
Since the given information is unknown and is NOT listed, which is the only conclusion that can be made
from the diagram created?
MACC.912.G-CO.3.9
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A.
B.
C.
D.
are complementary
7. In the figure below,
is parallel to
Which statement proves that
MACC.912.G-CO.3.9
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A.
If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
B.
If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.
C.
If two parallel lines are cut by a transversal, the corresponding angles are congruent.
D.
If two parallel lines are cut by a transversal, the vertical angles are congruent.
8. Consider this definition. A circle is the set of all points in a plane at a certain distance, its radius, from a
certain point, its center.
Which of the following words in the definition is an undefined term used in geometry?
MACC.912.G-CO.1.1
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A.
point
B.
radius
C.
center
D.
distance
9. In the diagram, which construction is being demonstrated?
MACC.912.G-CO.4.12
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A.
The first marks for constructing an altitude.
B.
The first marks for constructing an isosceles triangle.
C.
The first marks for constructing an equilateral triangle.
D.
The first marks for constructing a perpendicular bisector.
10. Given any three noncollinear points P, Q, and R, which geometric figure are we always able to construct?
MACC.912.G-CO.4.12
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A.
A circle with diameter PQ that passes through R
B.
A circle with center P and passing through Q and R
C.
A rectangle with vertices P and Q, whose diagonals intersect at R
D.
A triangle with vertices P, Q, and R
11. In this figure, lines a, b, c, d, and e intersect as shown.
Based on the angle measures, which pair of lines is parallel?
MACC.912.G-CO.3.9
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A.
a and b
B.
c and e
C.
c and d
D.
d and e
12. Which of the figures below is the correct construction of an angle bisector?
MACC.912.G-CO.4.12
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A.
B.
C.
D.
14. If
and
I
II
III
which is a valid conclusion?
are supplementary angles
are complementary angles
MACC.912.G-CO.3.9
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A.
I only
B.
I and II
C.
I and III
D.
I, II, and III
15. In the figure, Lines a and b are intersected by Line t.
Which of these statements proves that Lines a and b are parallel?
MACC.912.G-CO.3.9
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A.
B.
C.
D.
16. What are two lines that intersect to form right angles called?
MACC.912.G-CO.1.1
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A.
oblique
B.
parallel
C.
perpendicular
D.
skew
17. Which conjecture must be true?
MACC.912.G-CO.3.9
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A.
If two angles are adjacent angles, then the angles are supplementary.
B.
If two congruent angles are supplementary, then the angles are right angles.
C.
If two congruent angles have a common vertex, then the angles are vertical angles.
D.
If two angles are both acute angles, then the sum of the angle measures is less than 90°.
18. In the diagram, parallel lines b and c are cut by transversal t. The informal proof below the diagram lists the
reasons needed to justify
1.
since vertical angles are congruent.
2.
since _______.
3.
since vertical angles are congruent.
4.
due to the transitive property of equality. Which of the following is an acceptable justification
for Statement 2?
MACC.912.G-CO.3.9
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A.
vertical angles are congruent
B.
corresponding angles are congruent
C.
remote interior angles are congruent
D. alternate interior angles are congruent
19. Which statement describes two parallel lines?
MACC.912.G-CO.1.1
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A.
They do not intersect and they lie on the same plane.
B.
They do not intersect and they do not lie on the same plane.
C.
They intersect at a point and form right angles.
D.
They intersect at a point but do not form right angles.
20. Jordan has to prove the theorem that states: If two lines are cut by a transversal so that consecutive interior
angles are supplementary, then the lines are parallel.
She decides to solve it by indirect proof using the diagram below.
Which sentence should be Jordan’s first statement?
MACC.912.G-CO.3.9
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A.
Assume that Line r is not parallel to Line m.
B.
Assume
C.
Assume that Angles 1 and 2 are not consecutive.
D.
Assume
are not congruent.
are not supplementary.
21. Consider this proof:
Which reason could be used to justify Statement 3 in this proof?
MACC.912.G-CO.3.9
Webb: 1
A.
subtraction property of equality
B.
substitution property of equality
C.
definition of supplementary
D.
definition of complementary
22. The piece of art below was created with strings of different lengths strung in straight line segments across
the canvas. Angle 1 and Angle 2 are formed by the intersection of different strings, but both angles have a
measure of 72°.
Which statement about the geometric relationships formed by the strings in the art must be true?
MACC.912.G-CO.3.9
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A.
Angle 1 and Angle 2 are complementary angles.
B.
Angle 1 and Angle 2 are vertical angles.
C.
Line t and Line n are perpendicular.
D. Line s and Line t are parallel.
Student Name: ______________________
Teacher:
______________________
District:
Miami-Dade County Public Schools
Assessment:
9_12 Mathematics Geometry Exam 1
Description:
GEO Topic 2 Test: Transformations in the Plane
Form:
201
Date: ___________
1. Consider this proof:
Which reason could be used to justify Statement 3 in this proof?
MACC.912.G-CO.3.9
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A.
subtraction property of equality
B.
substitution property of equality
C.
definition of supplementary
D.
definition of complementary
2. Triangle QRS is shown on this grid.
Which graph shows
MACC.912.G-CO.1.2
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A.
B.
after it is rotated 180° clockwise about the origin?
C.
D.
3. Which transformation of a figure will create an image that is NOT congruent to the original figure?
MACC.912.G-CO.1.2
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A.
Dilation by a factor of 7
B.
C.
Translation by 5 units to the left on the x-axis
D.
Rotation by 180º
4. On a coordinate plane, each point on
counterclockwise to create
on
MACC.912.G-CO.1.4
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A.
B.
C.
D.
is defined by coordinates
The segment is rotated 90°
Which of the following defines a point on
that corresponds to a point
5. Segment PQ is mapped to segment
by a transformation. Line l is the perpendicular bisector of
. Which statement describes all the possible transformations that could be used for this mapping?
MACC.912.G-CO.1.4
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A.
only a rotation
B.
only a reflection
C.
only a translation
D. a rotation, a reflection, and a translation
6. Look at the figures below.
How was each point of Polygon ABCDE shifted to get Polygon A'B'C'D'E' ?
MACC.912.G-CO.1.2
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A.
right 1 unit and down 4 units
B.
right 1 unit and down 1 unit
C.
left 1 unit and up 4 units
D. left 1 unit and up 1 unit
and
7. A rotation about Point A maps Point B to
and Point C to
Which statement must be true?
MACC.912.G-CO.1.4
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A.
B.
C.
If Point B is
D.
If Point C is
then Point
must be
then Point
must be
8. A section of a leaded glass window is shown below.
Given:
• Each piece of lead in the glass is a straight line segment.
•
•
Which justification proves that
MACC.912.G-CO.3.9
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A. addition property
B.
transitive property
C.
vertical angles are congruent
D. alternate interior angles are congruent
9. The graph below represents which reflection?
MACC.912.G-CO.1.2
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A. about the x-axis
B.
about the y-axis
C.
about
D. about
10. Triangle JKL was translated to create
Which statement describes the translation of
MACC.912.G-CO.1.2
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A.
B.
C.
D.
as shown in the following graph.
13. Which type of transformation to the triangle has occurred from Graph 1 to Graph 2 in this diagram?
MACC.912.G-CO.1.5
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A.
rotation
B.
dilation
C.
reflection
D.
translation
14. If
and
I
II
III
which is a valid conclusion?
are supplementary angles
are complementary angles
MACC.912.G-CO.3.9
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A.
I only
B.
I and II
C.
I and III
D.
I, II, and III
15. Pentagon EFGHI is being relected over the dashed line
Pentagon E'F'G'H'I'.
in the coordinate plane below to create
What ordered pair will complete the reflection as Point H'?
MACC.912.G-CO.1.2
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A.
B.
C.
D.
16. A regular hexagon is rotated about its center. By which angle could the hexagon be rotated so that it is
mapped onto itself?
MAFS.912.G-CO.1.3
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A.
30°
B.
45°
C.
60°
D.
90°
17. Mr. Williams drew the image of a windmill with the perpendicular lines of symmetry shown below.
He asked two of his students what rotation about the center point, O, will result in an image that looks like
the original. Lara said 90° clockwise and Clark said 180°. Which student(s) answered correctly?
MAFS.912.G-CO.1.3
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A.
only Lara
B.
only Clark
C.
both Lara and Clark
D.
neither Lara nor Clark
18. Quadrilateral PQRS is translated to form Quadrilateral
MACC.912.G-CO.1.4
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A.
and
are parallel and congruent.
B.
and
are parallel but not congruent.
C.
and
are congruent but not parallel.
D.
and
are neither congruent nor parallel.
. Which statement must be true?
19. What is being constructed in the figure?
MACC.912.G-CO.4.12
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A.
B.
C.
D.
20. In the diagram below, which transformation could have been applied to
MACC.912.G-CO.1.5
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A.
reflection across the x-axis
B.
rotation 180° about the origin
C.
translation of
to
D.
translation of
to
to create L'P'R'?
21. Two transformations of Quadrilateral PQRS are described below.
• First transformation:
• Second transformation:
Which transformations were used on Quadrilateral PQRS?
MACC.912.G-CO.1.5
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A. a reflection over x-axis, then a translation
B.
a reflection over y-axis, then a translation
C.
a translation, then a reflection over x-axis
D. a translation, then a reflection over y-axis
22. In the figure, Lines a and b are intersected by Line t.
Which of these statements proves that Lines a and b are parallel?
MACC.912.G-CO.3.9
Webb: 1
A.
B.
C.
D.
Student Name: ______________________
Teacher:
______________________ Date: ___________
District:
Miami-Dade County Public Schools
Assessment:
9_12 Mathematics Geometry Benchmark 1
Description:
Geometry Topic 3
Form:
201
1. Yuri drew triangle ABC then reflected it over line m to create triangle WXY.
Yuri concludes that the triangles are congruent. Which is a correct validation for this
conclusion?
MAFS.912.G-CO.2.7
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A.
B.
C.
D.
When the triangle was reflected, the height of the resulting triangle is parallel to the
height of the original triangle.
When the triangle was reflected, the base of the resulting triangle lies on the same line
as the base of the original triangle.
When the triangle was reflected, the corresponding sides and angle measures of the
resulting triangle are the same as the original triangle.
When the triangle was reflected, the corresponding sides of the resulting triangle have
slopes that are opposite to the slopes of the original triangle.
2. Sam is studying a geometric drawing. He observes that
vertical angles and that
and
and
are obtuse
are congruent. He proves that
Which
postulate uses Sam's information to prove that
MAFS.912.G-CO.2.8
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A.
Angle-Side-Angle (ASA)
B.
Hypotenuse Leg (HL)
C.
Side-Side-Angle (SAS)
D.
Side-Side-Side (SSS)
is transformed on a coordinate plane to obtain its congruent image
3.
of the following statements could be true?
I.
is the translated image of
II.
is the reflected image of
III.
is the rotated image of
MAFS.912.G-CO.2.6
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A.
only I
B.
only II
C.
I, II, and III
D.
only I and II
Which
4. Figure 1 is reflected across a vertical line, translated up, and rotated counterclockwise
fewer than 90 degrees. The resulting figure is represented by Figure 2, as shown below.
Which angle MUST be congruent to
MAFS.912.G-CO.2.7
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A.
B.
C.
D.
5. In the figure below,
is a reflected image of
Anne states that reflections preserve side lengths, so
and
therefore the triangles are congruent.
Tim states that reflections preserve angle measures, so
therefore the triangles are congruent.
Who is correct?
MAFS.912.G-CO.2.7
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A.
neither Anne nor Tim
B.
both Anne and Tim
C.
only Anne
D.
only Tim
and
6. The figure below shows
If
and
and
on a coordinate plane.
units, which statement is true?
MAFS.912.G-CO.2.7
Webb: 1
A.
B.
The triangles are similar because dilations preserve only angle measure, so
The triangles are similar because dilations preserve only angle measure, so
C.
The triangles are congruent because they can be mapped onto each other through
reflection, so
and
units.
D.
The triangles are congruent because they can be mapped onto each other through
reflection, so
and
units.
7. What is the perimeter of the rectangle shown on the coordinate grid?
MAFS.912.G-GPE.2.7
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A.
12 units
B.
15 units
C.
24 units
D.
30 units
8. In triangle
theorem?
MAFS.912.G-CO.3.10
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A.
B.
C.
D.
and
Which of these can be proved using the triangle sum
9. A triangle ABC and its translated image XYZ are shown below.
What relationship CANNOT be used to prove that triangle ABC is congruent to triangle
XYZ?
MAFS.912.G-CO.2.8
Webb: 1
A.
Angle-Angle-Angle
B.
Angle-Side-Angle
C.
Side-Angle-Side
D.
Side-Side-Side
10. A rectangle on a coordinate grid has vertices at
and
The rectangle
is rotated 90° clockwise about the origin and then translated 6 units up and 2 units right.
Which graph correctly shows the transformed rectangle?
MAFS.912.G-CO.2.6
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A.
B.
C.
D.
11. Which of these would prove that triangle PQS is congruent to triangle RQT?
MAFS.912.G-CO.2.8
Webb: 2
A. Triangle PQS is a dilation of triangle RQT, so the triangles are congruent by AAA.
B.
Triangle PQS is a dilation of triangle RQT, so the triangles are congruent by SSS.
C.
Triangle PQS is a reflection of triangle RQT, so the triangles are congruent by SSS.
D. Triangle PQS is a reflection of triangle RQT, so the triangles are congruent by AAA.
12. Which sequence of transformations will result in an image that is NOT congruent to
graphed on the coordinate grid below?
MAFS.912.G-CO.2.6
Webb: 2
A.
a translation 4 units to the left followed by a reflection across the x-axis
B.
a reflection across the y-axis followed by a rotation 90° clockwise about the origin
C.
a dilation by a scale factor of 2 about the origin, followed by a translation 3 units down
D.
a rotation 90° clockwise about the origin followed by a dilation by a scale factor of 1
about the origin
13. Mike wants to prove that the diagonals of parallelogram JORD bisect each other. To do
that, he labels the intersection of the diagonals as point N and composes the proof
shown below.
Step
Justification
1 JORD is a parallelogram.
Given
2
Opposite sides of a parallelogram are congruent.
3
?
Definition of a parallelogram
4
and
?
?
5
6
and
Corresponding parts of congruent triangles are
congruent.
7
and
Definition of congruent line segments
8 N is the midpoint of
bisects
9
and
and
Definition of midpoint
bisects
Definition of segment bisector
The statement of step 3, and the justifications for steps 4 and 5, are missing from this
copy. Which set of statements correctly completes Mike’s proof?
MAFS.912.G-CO.3.10
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A.
B.
C.
D.
14. Given the figure below, which one piece of evidence would allow the triangles to be
proven congruent?
MAFS.912.G-CO.2.7
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A.
B.
C.
was reflected over line
to result in
D.
was dilated about a point on line
to result in
15. On a set of parallel lines cut by a transversal,
value of x could show that
and
are corresponding angles, and why?
MAFS.912.G-CO.3.9
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A.
B.
C.
D.
and
Corresponding angles are congruent.
Corresponding angles are congruent.
Corresponding angles are supplementary.
Corresponding angles are supplementary.
Which
16. Triangle
is located in the third quadrant of a coordinate plane. If triangle
reflected across the y-axis to obtain triangle,
is
which statement is true?
MAFS.912.G-CO.2.6
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A.
lies in quadrant II and is congruent to
B.
lies in quadrant IV and is congruent to
C.
lies in quadrant II and is not congruent to
D.
lies in quadrant IV and is not congruent to
17. Patricia uses the given isosceles triangle ABC to prove that the base angles of an
isosceles triangle are congruent. The statements associated with the proof are listed
below.
Which of these reasons does NOT justify any of the statements given above?
MAFS.912.G-CO.3.10
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A.
CPCTC
B.
reflexive property
C.
SAS postulate of congruence
D.
definition of perpendicular lines
18. Maggie drew triangle ABC and then drew triangle DBE.
Triangle ABC is congruent to triangle DBE only if
MAFS.912.G-CO.2.7
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A.
29°
B.
55°
C.
62°
D.
89°
19.
MAFS.912.G-CO.2.7
Webb: 1
A.
B.
C.
D.
Which statement must be true?
is equal to what value?
20. Use the given triangles to answer the question.
Triangle JKL is reflected across line a to form triangle MNO. Which one of these is true?
MAFS.912.G-CO.2.7
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A.
B.
C.
D.
21. The figure below shows isosceles triangle ABC, with
Which is a valid proof that shows
MAFS.912.G-CO.3.10
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A.
B.
C.
D.
?
and
bisecting
22. The statements of a two-column proof are listed below.
What should the corresponding reasons be?
MAFS.912.G-CO.3.10
Webb: 2
A.
B.
C.
D.
1. Given; 2. Definition of congruency; 3. Definition of congruency; 4. SAS theorem; 5.
CPCTC
1. Given; 2. Definition of congruency; 3. Reflexive property; 4. Hypotenuse-leg theorem;
5. CPCTC
1. Given; 2. Definition of perpendicular lines; 3. Definition of congruency; 4. SAS
theorem; 5. CPCTC
1. Given; 2. Definition of perpendicular lines; 3. Reflexive property; 4. Hypotenuse-leg
theorem; 5. CPCTC
23. In the graph below,
is transformed to obtain
To show that the triangles are congruent, triangle
could be transformed by which
movement(s) to fit exactly on triangle
MAFS.912.G-CO.2.6
Webb: 2
a rotation of 180° clockwise about the origin followed by a dilation of 1.2 with the
center of dilation at the origin
a rotation of 90° clockwise about the origin followed by translations down 1 unit and
B.
left 10 units
a rotation of 270° clockwise about the origin followed by translations left 1 unit and up
C.
10 units
D. a reflection over the x-axis followed by a reflection over the y-axis
A.
24. In the figure below,
is rotated and reflected to obtain
If Amy knows that
which statement correctly lists additional information she would need to
prove the relationship between these triangles?
MAFS.912.G-CO.2.8
Webb: 2
A.
Reflections and rotations preserve angle measures but not side lengths, so showing
can prove that the given triangles are similar by AA.
B.
Reflections and rotations preserve angle measures but not side lengths, so showing
can prove that the given triangles are similar by AA.
C.
Reflections and rotations preserve side lengths and angle measures, so showing
and
can prove that the given triangles are congruent by SSA.
D.
Reflections and rotations preserve side lengths and angle measures, so showing
and
can prove that the given triangles are congruent by SAS.
25. Elizabeth wants to prove the triangle angle sum theorem. Which steps could be part of
her proof?
MAFS.912.G-CO.3.10
Webb: 2
A.
B.
C.
D.
Construct an altitude of one side, and then use corresponding parts of congruent
triangles.
Construct a line perpendicular to two sides of the triangle, and then use the linear pair
postulate.
Construct a line passing through a vertex and parallel to the base of the triangle, and
then use alternate interior angles.
Construct a line passing through two sides of the triangle and parallel to the base of
the triangle, and then use corresponding angles.