Download 340678_TestBooklet math 2 GCO

TEST NAME: Math II Geometry GCO
TEST ID: 340678
GRADE: 09 ­ 10
SUBJECT: Mathematics
TEST CATEGORY: My Classroom
Math II Geometry GCO
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11/19/14, Math II Geometry GCO
Student: Class:
Date:
Read the passage ­ 'Quilt Making' ­ and answer the question below:
Quilt Making
Quilt Making
Many years ago quilts were made from scraps of fabric to use on beds for warmth. Sewing the
pieces of fabric together was called “piecing” the quilt. The pieces of fabric were frequently
squares or triangles. The old pieced quilts are greatly valued today as works of art. Making
quilts from the old patterns is a popular hobby.
Natalie makes quilts using some of the old patterns. The following figures show the stages for
one of the patterns Natalie will use for a new quilt.
Figure 1 shows a pattern that begins with a square and four congruent triangles. The square is
4 inches on each side. The triangles are isosceles with a height of 2 inches, and the vertex
angle is a right angle. Natalie will cut the square from one color and the four triangles from a
different color or pattern.
Figure 2 shows four more triangles that are cut from a different color or pattern being added to
the first figure. The new triangles are isosceles with a right angle at the vertex.
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A completed pattern is called one “square.” Natalie will make 20 squares for her quilt and will
stitch them together in a 4­by­5 array.
She adds 0.25 inch to each side of each square to create a seam when she sews the squares
together. To finish the quilt, she sews a border that is 4 inches wide around the outside of the
entire array.
It takes Natalie a long time to make her quilt, but she has something beautiful for her bed
when it is complete.
1.
Read "Quilt Making" and answer the question.
Figure 1 is reflected over and then reflected over Which
transformation would result in the same image?
A.
reflecting Figure 1 over and rotating clockwise around the
center of square ABCD
B.
reflecting Figure 1 over and rotating clockwise around the
center of square ABCD
C.
rotating Figure 1 D.
rotating Figure 1 clockwise around the center of square ABCD
clockwise around the center of square ABCD
Read the passage ­ 'Quilt Making' ­ and answer the question below:
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2.
Read "Quilt Making" and answer the question.
The definition of congruence states two figures are congruent if one
figure can be mapped onto the other through a sequence of rigid motions.
According to this definition, which rigid motions could Natalie use to
prove all four triangles in Figure 1 are congruent?
A.
Dilate each triangle by a scale factor of 4 around the center of the
square ABCD, which results in corresponding sides and angles being
congruent.
B.
Rotate each triangle around the center of the square ABCD, which
results in corresponding sides and angles being congruent.
C.
Translate each triangle vertically and/or horizontally, which results in
corresponding sides and angles being congruent.
D.
Reflect each triangle vertically and/or horizontally, which results in
corresponding sides and angles being congruent.
3. Which transformation does not preserve distance?
A.
B.
C.
D.
4.
Point lies at Point is reflected over the y­axis and then
translated 7 units down to produce to produce from Which rule could have been used
A.
B.
C.
D.
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5. A transformation to the graph of a function, takes the function and translates it left 5
units. Which equation represents A.
B.
C.
D.
6.
A function f(x) is described by the ordered pairs If the given
function is translated 2 units to the right and then reflected across the x­
axis, what are the ordered pairs that describe the transformed function?
A.
B.
C.
D.
7.
Figure D is a regular polygon. If D is rotated not concurrent with D, but if D is rotated the resulting figure is
then the resulting figure is
concurrent with D. Which shape could D be?
A.
A 9­sided polygon
B.
An 18­sided polygon
C.
A 20­sided polygon
D.
A 36­sided polygon
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8.
A regular polygon has n sides. Which algebraic expression represents the
number of degrees of rotation around its center that would carry the
polygon onto itself?
A.
B.
C.
D.
9.
The figure below shows line segments a and b passing through a regular
pentagon.
Which statement describes a series of transformations that will result
in a pentagon that is mapped onto the one shown?
A.
rotating the pentagon 72° clockwise about its center and
then reflecting it across segment a
B.
rotating the pentagon 72° clockwise about its center
and then reflecting it across segment b C.
rotating the pentagon 90° clockwise about its center and
then reflecting it across segment a
D.
rotating the pentagon 90° clockwise about its center
and then reflecting it across segment b
10. Which number of degrees could a regular hexagon be rotated around its center to not carry it back onto itself?
A.
60°
B.
120°
C.
150°
D.
180°
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11.
The opposite sides of a certain quadrilateral are congruent to each other
and parallel to each other. The midpoints of two opposite sides are
connected to form a midsegment. Which of these statements is always
true?
A.
Reflecting the quadrilateral across its midsegment carries the
quadrilateral onto itself.
B.
Rotating the quadrilateral by 90º counterclockwise about the midpoint
of its midsegment will carry it onto itself.
C.
Reflecting the quadrilateral across its midsegment carries the
quadrilateral onto itself only if the adjacent angles of the
quadrilateral are congruent.
D.
Rotating the quadrilateral by 90º counterclockwise about the midpoint
of its midsegment will carry it onto itself only if the adjacent angles
of the quadrilateral are congruent.
12. A trapezoid is graphed on the coordinate plane.
Which transformation maps the trapezoid onto itself?
A.
rotation of 90°
B.
rotation of 180°
C.
reflection over the x­axis
D.
reflection over the y­axis
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13.
Rectangle ABCD is shown on the coordinate grid below.
Which sequence of reflections will map rectangle ABCD onto itself?
A.
a reflection over the x­axis followed by a reflection over the y­axis
B.
a reflection over the x­axis followed by another reflection over the
x­axis
C.
a reflection over the line followed by a reflection over the line D.
a reflection over the line followed by a reflection over the line 14. Which transformation would map a rectangle onto itself?
A.
reflection over a diagonal
B.
reflection over the shorter side
C.
rotation of 40° around its center
D.
rotation of 180° around its center
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15.
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? A.
only Lara
B.
only Clark
C.
both Lara and Clark
D.
neither Lara nor Clark
16.
A regular hexagon is rotated on a coordinate plane. Which rotation would
result in a hexagon with vertices at the same coordinates as the vertices
of the original hexagon?
A.
a 60º clockwise rotation about the center of the hexagon
B.
a 90° clockwise rotation about the center of the hexagon
C.
a 60° clockwise rotation about one of the vertices of the hexagon
D.
a 90° clockwise rotation about one of the vertices of the hexagon
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17.
Line segment shown below, is reflected over the y­axis to form the
line segment Rhoda concludes that the y­axis is a perpendicular bisector of Andy concludes that the lines and and
are parallel. Whose conclusion is
correct?
A.
neither Rhoda’s nor Andy’s
B.
both Rhoda’s and Andy’s
C.
only Rhoda’s
D.
only Andy’s
18.
Which of these statements is NOT correct?
A.
A composition of reflections across two intersecting lines is
equivalent to a rotation.
B.
A composition of reflections across three parallel lines is equivalent
to one reflection.
C.
A composition of reflections across two parallel lines is equivalent to
a translation.
D.
A composition of reflections across two intersecting lines is
equivalent to a translation.
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19.
Square ABCD, shown on the graph below, is rotated 90° counterclockwise
about point A to form square Which statement best describes line segments and A.
and are parallel.
B.
and are perpendicular.
C.
and lie on the same line.
D.
and intersect but are not perpendicular to each other.
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20.
Line segment n is shown on the coordinate plane below.
Which transformation would result in a line segment, perpendicular to n?
A.
a reflection across the x­axis
B.
a reflection across the y­axis
C.
a 90° clockwise rotation about the point D.
a 180° counterclockwise rotation about the point that is
21.
Clarisse drew line segment and then translated it 3 units to the right
and 4 units down to form line segment She then connected and and and to form two more line segments. Which statement(s) about
the resulting figure must be true?
I. II. III. is a rectangle.
A.
I only
B.
III only
C.
I and II only
D.
I, II, and III
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22. The diagram shows an angle and its image after a transformation.
Which definition describes this transformation?
A.
a transformation that flips a figure across a line
B.
a transformation that turns a figure around a point
C.
a transformation that copies a figure directly over the existing figure
D.
a transformation that slides each point of a figure the same distance in the same direction
23. What is a definition of a translation of a polygon?
A.
Each point of the polygon moves parallel to, and the same distance as, every other point.
B.
Each point of the polygon moves perpendicular to, and the same distance as, every other point.
C.
Each point of the polygon moves the same distance in the same direction along a circle with the same
radius.
D.
Each point of the polygon moves the same distance in the same direction along a perpendicular bisector
of a side of the polygon.
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24.
Triangle with vertices coordinate plane below. is graphed on the
Which transformation of would yield so that is parallel
to A.
a 180° clockwise rotation about the origin
B.
a 90° counterclockwise rotation about the origin
C.
a reflection across the y­axis
D.
a reflection across the x­axis
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25. Figure 1 is mapped to Figure 2 under a transformation.
Which series of transformations maps Figure 1 to Figure 2?
A.
reflection over the y­axis and a reflection over the x­axis
B.
reflection over the y­axis and a translation of 2 units down
C.
rotation of 90° counter­clockwise around the origin and a reflection across the y­axis
D.
rotation of 90° clockwise around the origin and a translation of 2 units down
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26.
On the coordinate plane, the location of across the line across the line is found by reflecting is found by reflecting Which ordered pair corresponds with the location of A.
B.
C.
D.
27. The parallelogram graphed on the coordinate plane is rotated 90° counterclockwise about the origin.
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Which is the image of the parallelogram after this rotation?
A.
B.
C.
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D.
28.
The triangle shown below is reflected across line l. It is then rotated 90º
counterclockwise about the origin and then translated 2 units to the left
to obtain triangle Which figure correctly shows A.
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B.
C.
D.
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29. Triangle RST is translated 4 units right and 2 units down.
What are the coordinates of point R?
A.
B.
C.
D.
30.
Triangle ABC is shown on the coordinate plane below. The triangle is
reflected across the y­axis and then translated 3 units to the right to
form triangle Which coordinate plane shows triangle Math II Geometry GCO
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A.
B.
C.
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D.
31. Figure 2 is a transformation of Figure 1.
Which series of transformations map Figure 1 to Figure 2?
A.
a reflection across the x­axis and a translation 2 units right
B.
a reflection across the y­axis and a translation 2 units down
C.
a rotation of 90° clockwise about the origin and a translation 2 units down
D.
a rotation of 90° counterclockwise about the origin and a translation 2 units down
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32.
If is rotated 90 degrees clockwise about the origin and then
translated 1 unit up and 2 units to the left, what are the endpoints of
the resulting image?
A.
B.
C.
D.
33.
George designs a computer program that can easily perform any number
of transformations. To check his program, he enters the coordinates of
the vertices of a quadrilateral as He
then types instructions to reflect the quadrilateral across the x­axis 99
times and then across the y­axis 99 times. Which figure shows the
transformed quadrilateral generated by the program?
A.
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B.
C.
D.
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34.
Triangle ABC has vertices at It is
translated 1 unit left and 2 units up to form triangle vertices of triangle What are the
A.
B.
C.
D.
35.
Which series of transformations can be used to prove that is congruent to as shown by the graphs below?
A.
rotate 90° counterclockwise about the origin and then translate
it 8 units to the right
B.
reflect the left
across the line and then translate it 4 units to
C.
rotate 90° clockwise about the origin and then reflect it across that resulted from the rotation
D.
reflect across the line and then reflect it across that
resulted from the first reflection
36.
The figure below shows plotted on a coordinate plane. The triangle
is first rotated by 90° counterclockwise about the origin and is then
reflected about the line Math II Geometry GCO
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Which graph shows the transformed triangle?
A.
B.
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C.
D.
37.
Which transformation maps each triangle in the xy­coodinate plane to a
congruent triangle?
A.
B.
C.
D.
38.
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?
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A.
B.
C.
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D.
39.
Use the image to answer the question below.
Which series of transformations would result in a figure that is congruent
to the triangle ABC?
A.
rotation of clockwise about the origin and then dilation with a
scale factor of centered at the origin
B.
rotation of clockwise about the origin and then dilation with a
scale factor of 2, centered at the origin
C.
reflection across the line centered at the origin
D.
translation 3 units to right and then dilation with a scale factor of 3,
centered at the origin
and then dilation with a scale factor of 40.
Quadrilateral Math II Geometry GCO
shown on the coordinate plane below, is reflected
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over the y­axis to form quadrilateral Which of these shows the correct location of quadrilateral A.
B.
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C.
D.
41.
Triangle is located in the third quadrant of a coordinate plane. If
triangle is reflected across the y­axis to obtain triangle, which
statement is true?
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 Math II Geometry GCO
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42.
Maggie drew triangle ABC and then drew triangle DBE.
Triangle ABC is congruent to triangle DBE only if is equal to what
value?
A.
29°
B.
55°
C.
62°
D.
89°
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43.
Triangle ABC was reflected over the x­axis and then reflected over the y­
axis to form the triangle with vertices labeled M, N, and P in the
coordinate plane below.
Based on these reflections, which statements would prove that the
triangles are congruent?
A.
B.
C.
D.
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44. Triangle JKL and line segment RT are shown on the graph.
If triangle JKL is congruent to triangle RST, what is the maximum number of possible coordinates for point S?
A.
1
B.
2
C.
3
D.
4
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45.
The figure below shows and on a coordinate plane. If and units, which statement is true?
A.
The triangles are similar because dilations preserve only angle
measure, so B.
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.
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46.
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 A.
B.
C.
D.
47.
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?
A.
B.
C.
D.
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48.
A triangle, PQR, is reflected across the x­axis and translated 3 units up
to form triangle MNO.
Which statement is true?
A.
The corresponding sides and angles of the given triangles are
congruent.
B.
Only the corresponding angles of the given triangles are congruent.
C.
Only the corresponding sides of the given triangles are congruent.
D.
Only the base lengths of the triangles are congruent.
49. If triangle RST is congruent to triangle WXY, by the Angle­Side­Angle Theorem, which transformation would not
map triangle RST to triangle WXY?
A.
horizontal shift 4 units left
B.
reflection across the y­axis
C.
dilation with a scale factor of 3
D.
rotation of 90° around the origin
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50.
In the figure below, If Amy knows that is rotated and reflected to obtain which statement correctly lists
additional information she would need to prove the relationship between
these triangles?
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.
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51.
In the figure below, is a reflection of Two students describe the given triangles as shown:
Student I: Because reflections preserve side lengths, so and
by SSS.
Student II: Because reflections preserve both side lengths and angle
measures, and so by SAS.
Who has proven correctly?
A.
only student I
B.
only student II
C.
both student I and student II
D.
neither student I nor student II
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52.
The figure below shows and its reflection Based on this reflection, which of these can be used to prove A.
B.
C.
D.
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53.
James is practicing proving geometric theorems. He writes the
statements needed for the proof below in different boxes and mixes
them up so they are not in order.
In what order could James arrange the statements to make the proof
correct?
A.
1, 3, 5, 6, 4, 7, 2, 8
B.
1, 3, 5, 6, 2, 4, 7, 8
C.
3, 5, 6, 7, 1, 4, 2, 8
D.
3, 1, 5, 6, 7, 2, 4, 8
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54. In the diagram, line l is parallel to line m. When proving that the sum of the measures of the angles of a triangle
is 180°, it is stated that because Why is this true?
A.
and because alternate interior angles are supplementary if lines are
B.
and because alternate interior angles are congruent if lines are parallel.
C.
and because corresponding angles are congruent if lines are parallel.
D.
and because same­side interior angles are congruent if lines are parallel.
parallel.
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55.
A proof of the base angle theorem is shown. Which statements correctly complete the proof?
A.
B.
C.
D.
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56.
In triangle and Which of these can be proved
using the triangle sum theorem?
A.
B.
C.
D.
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57.
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
1 JORD is a parallelogram.
Given
2
Opposite sides of a parallelogram are congruent.
?
and 3
4
Justification
Definition of a parallelogram
?
5
?
6
and 7
and Corresponding parts of congruent triangles are
congruent.
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?
A.
B.
C.
D.
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58.
John writes the proof below to show that the sum of the angles in a
triangle is equal to 180º.
Which of these reasons would John NOT need to use in his proof?
A.
The sum of the angles on one side of a straight line is 180º.
B.
If a statement about a is true and replacing a with b is also true.
C.
When two parallel lines are cut by a transversal, the resulting
alternate interior angles are congruent.
D.
When two parallel lines are cut by a transversal, the resulting
alternate exterior angles are congruent.
the statement formed by
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