Unit One Test (Transparallellines)
Name:_____________________________________________
Date:________________________
1. The coordinate grid shows the intersection of line 1 and line 2.
Which transformations on lines 1 and 2 will result in a pair of lines intersecting at the same angle measurements as
those formed by the intersection of line 1 and line 2?
A. The reflection of line 1 over the x -axis and the translation of line 2 four units up.
B. The reflection of line 1 over the x -axis and the translation of line 2 four units to the left.
C. The reflection of line 1 over the x -axis and the reflection of line 2 over the line
D. The reflection of line 1 over the x -axis and the reflection of line 2 over the line
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Unit One Test (Transparallellines)
2. Lines m and n are graphed on the coordinate grid shown.
Part A
Lines m and n are translated 4 units down and 8 units left. Sketch a graph to represent the new location of lines m and
n . Label the new location of line m as line e and the new location of line n as line f .
Part B
Lines m and n are reflected across the x -axis. Explain the effect this reflection has on the lines. Has the distance
between the lines changed?
Part C
Are the lines m and n parallel, perpendicular, or intersecting lines? Describe what happens to the lines after a
clockwise rotation of 90° is applied to the lines.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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Unit One Test (Transparallellines)
3. Right triangle JKL is graphed on a coordinate grid.
Part A
If the triangle is reflected across the y -axis, what would be the vertices of the reflected triangle? Label the new
vertices as
and
Part B
What are the lengths of line segments JK and KL ?
Part C
What is the length of line segment
Show your work.
Part D
What is the relationship of triangles JKL and
Explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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Unit One Test (Transparallellines)
4. Which transformation can result in a new figure that is not congruent to the original figure?
A. dilation
B. reflection
C. rotation
D. translation
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Unit One Test (Transparallellines)
5. Mr. Novak draws a figure on a coordinate grid. He begins to construct a new figure congruent to the figure shown
by points
and
as shown in the coordinate grid.
Part A
Mr. Novak used two different transformations to create the new figure. Based on the location of points
what would be the coordinates of
and
and
Part B
Describe a sequence of transformations which would result in the new figure being congruent to the original figure
based on point
and
Part C
Create a similar figure, but not congruent, to Mr. Novak’s new figure in quadrant I. What are the coordinates of
and
Part D
Describe the sequence of transformations you used to create the figure in Part C.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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Unit One Test (Transparallellines)
6.
Fill in the blank. All ___________ are either similar or congruent to each other.
A. circles
B. triangles
C. rectangles
D. parallelograms
7.
A city park has two congruent flowerbeds. The flowerbeds are shown as triangles PQR and STU. Which angle is
congruent to P?
A.
B.
C.
D.
R
S
T
U
8.
The triangles shown are congruent. Which of the following two sides MUST be proportional?
A. CM and SV
B. CM and MT
C. CT and VU
D. CT and MT
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Unit One Test (Transparallellines)
9. A marine scientist is looking for a specific organism in the ocean. The triangle shows the part of the ocean the
scientist previously studied.
The scientist needs to modify his location. The triangle will be reflected over the line
a vertex of the reflected triangle?
Which coordinate is
A.
B.
C.
D.
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Unit One Test (Transparallellines)
10. A graphic artist is creating a design with two rectangles. The grid shows the first rectangle.
The artist wants to rotate the first rectangle
rectangle?
about the origin. Which coordinate is a vertex of the second
A.
B.
C.
D.
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Unit One Test (Transparallellines)
11. The diagram below shows the location of
Suppose that
on a coordinate plane.
is rotated 180° clockwise about the origin. What are the coordinates of the image of point E?
A. (–2, –4)
B. (–4, –2)
C. (4, –2)
D. (–4, 2)
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Unit One Test (Transparallellines)
12. Look at the triangles below.
Which of these triangles are most likely similar?
A. 1 and 2
B. 1 and 3
C. 2 and 3
D. 3 and 4
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Unit One Test (Transparallellines)
13. Rectangle P and rectangle Q are graphed on a coordinate grid.
Part A
Describe a sequence of at least two transformations that would prove or disprove whether or not rectangle P and
rectangle Q are similar.
Part B
Rectangle Q is dilated using a scale factor of 3 to become rectangle R. What are the coordinates of the vertices for
rectangle R?
Part C
The vertices of rectangle S are located at points
to rectangle P? Explain your answer.
and
Is rectangle S congruent
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
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Unit One Test (Transparallellines)
14. Rectangle A is shown on the coordinate grid.
Part A
Rectangle A is dilated by a factor of 0.5 about the center point
The new rectangle formed is rectangle B .
Create a coordinate grid similar to the one shown above. Graph and label rectangle B on the coordinate grid you
created.
Part B
Rectangle B is reflected across the y -axis to form rectangle C. Write the coordinates of each vertex of rectangle C.
Explain how the coordinates change when rectangle B is reflected across the y -axis to form rectangle C.
Part C
Rectangle A is rotated
counter-clockwise about the origin to form rectangle D. Graph and label rectangle D on
the same coordinate grid you created in Part A.
Part D
Is rectangle D similar to rectangle B? Explain your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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Unit One Test (Transparallellines)
15. Roger has a 3-inch-by-5-inch photograph. He is a good painter and wants to make a painting that looks exactly
like the photograph but larger. Which one of the following canvases should he buy for this painting?
A. 15 inches by 45 inches
B. 18 inches by 20 inches
C. 24 inches by 40 inches
D. 30 inches by 75 inches
16.
Susan has two boxes. Each box is 12 cm high, 12 cm long, and 12 cm wide. Which statement describes Susan's
boxes?
A. The boxes are congruent, but not similar.
B. The boxes are similar, but not congruent.
C. The boxes are similar and congruent.
D. The boxes are only similar.
17.
Given: ABC ~ DEF.
Which statement shown is a correct similarity statement?
A.
B.
C.
D.
BCA ~
BAC ~
CBA ~
CBA ~
EDF
EDF
DFE
FDE
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Unit One Test (Transparallellines)
18. Line segments PS and QT intersect at point R . Point R is a vertex of right triangle RPQ .
Part A
What is the measure of angle PQR ? Show your work and explain your answer.
Part B
What is the length of segment RQ ? Show your work.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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Unit One Test (Transparallellines)
19. Triangles DEF and JKL are shown.
Part A
What information is provided to show triangle DEF is similar to triangle JKL ?
Part B
What series of transformations could be used to obtain triangle JKL from DEF ?
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
________________________________________________________________________
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Unit One Test (Transparallellines)
20.
A.
B.
C.
D.
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Unit One Test (Transparallellines)
Answer Key
1. D) The reflection of line 1 over the x -axis and the reflection of line 2 over the line
2.
3.
4. A) dilation
5.
6. A) circles
7. B) S
8. A) CM and SV
9. C)
10. A)
11. B) (–4, –2)
12. B) 1 and 3
13.
14.
15. C) 24 inches by 40 inches
16. C) The boxes are similar and congruent.
17. B) BAC ~ EDF
18.
19.
20. D)
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