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Unit 1 – State Practice Test Problems
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Name: ________________
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13. A figure lies in Quadrant II of a coordinate plane. The figure is transformed by first reflecting across the
x-axis and then rotating 90 clockwise about the origin. In what quadrant will the image lie?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
14. What is the effect of the transformation described by the rule (x, y)  (y, x)?
A reflection across the y-axis
A reflection across the x-axis
A rotation 90 clockwise about the origin
A rotation 90 counterclockwise about the origin
15. A triangle has vertices (4, 1), (3, 0), and (7, 2). What are the vertices of the image of the triangle
after a reflection across the y-axis?
(4, 1), (3, 0), (7, 2)
(4, 1), (3, 0), (7, 2)
(4, 1), (3, 0), (7, 2)
(1, 4), (0, 3), (2, 7)
16. What can be concluded if 1 7?
tp
pq
pq
pt
17. In the proof shown here about equilateral
triangle XYZ, what is the correct reason that
can be used for Step 2 and Step 3?
Given: XY  YZ  XZ
Prove: X  Y  Z
The sum of the interior angles in a triangle is 180
If two sides of a triangle are congruent, then the angles opposite the sides are congruent.
If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
SSS congruence criterion
18. Which of the following statements can be concluded from the given triangle?
mU  mT
US  UT
US  ST
mU  mS
STU is an isosceles triangle.
mT  mS
ST  UT
STU is an equilateral triangle.
19. Match each statement in the proof with the correct reason.
Given: AB  AC, M is the midpoint of BC
Prove: B  C
A Definition of midpoint
B SAS congruence criterion
C Corresponding parts of congruent triangles
are congruent.
D SSS congruence criterion
E Definition of perpendicular bisector
F Given
G If a point is on the bisector of an angle, it is
equidistant from the sides of the angle.
H Reflexive property of congruence
____ 3. AB  AC
____ 4. BM  MC
____ 5. AM  AM
____ 6.
ABM 
ACM
____ 7. B  C
20. What is a valid reason for Step 2?
Given: ABCD is a parallelogram.
Prove: A  C; B  D
Definition of parallelogram
When parallel lines are cut by a transversal, alternate interior angles are congruent.
When parallel lines are cut by a transversal, corresponding angles are congruent.
Corresponding parts of congruent triangles are congruent.
21. Given AB  CD and AD  BC, what triangle congruence criterion is likely to be used in a proof that
AB  CD and AD  BC ?
SSS
AAS
ASA
SAS
22. Which conclusions are valid given ABCD is a parallelogram?
A  C
AB  CD
AC  BD
A and B are supplementary.
A  B
AC  BD
23. What is the first step to copy AB onto the line shown here?
¨
Use a straightedge to draw AB so it intersects the other line.
Open a compass to distance AB.
Use a ruler to measure AB.
Use a straightedge to draw AC.
24. AB with length 2.4 cm is dilated with scale factor 3. What is the length of the image, A¢ B¢ ?
25.
0.8 cm
2.4 cm
5.4 cm
7.2 cm
NOP has side lengths 5 cm, 7 cm, and 9 cm. If
lengths of the sides of
NOP 
RST, which of the following could be the
RST?
1 cm, 3 cm, 5 cm
6 cm, 8.4 cm, and 13.5 cm
7.5 cm, 10.5 cm, 13.5 cm
15 cm, 17 cm, and 19 cm
26. Which of the following dilations with center A can be used to show that
Map
ABC to
Map
ABC to
1
.
2
ADE using a dilation with scale factor 2.
Map
ADE to
ABC using a dilation with scale factor
Map
ADE to
ABC 
ADE using a dilation with scale factor
1
.
2
ABC using a dilation with scale factor 2.
¨
¨
27. Which of the following proportions could be used as a given to show that AB DF?
DE AE
=
DF AB
DA FB
=
AE BE
DA AE
=
BE BE
EF EB
=
DF AB
ADE?
28. A jogging path runs along the river from point C to point E, passing
through point A. You want to find the distance DE across a river using
indirect measurement. Which congruence criterion can be used to
show that ABC  ADE?
SSS
ASA
SAS
HL
29. In order to measure the height of a large tree,
Adrian measures the tree’s shadow and immediately
measures the length of his shadow and his height.
What is the height of the tree?
31.725 ft
42.3 ft
47.9 ft
56.4 ft
CONSTRUCTED RESPONSE
30. Is there a unique sequence of rigid motions that maps
ABC to
31. Determine whether the triangles are congruent by describing
a rigid motion that maps the black triangle to the gray triangle,
if one exists. Give a detailed description of the rigid motion.
MNP ? Explain your reasoning.
32. Use the figure below to answer parts a through c.
a. Draw the image of the figure after a 90 counterclockwise
rotation about the origin.
b. Draw the image of the figure from part a after the translation
(x, y)  (x  5, y  4).
c. Is the result from part b the same as the result of translating
the original figure using (x, y)  (x  5, y  4). followed by
rotating it 90 counterclockwise about the origin?
Explain your reasoning.
33.Given
IJK @
LMN, find the length of all unlabeled sides and the measure of all unlabeled angles.
34. In the figure below, line p is parallel to line q. Find the measures
of 2 and 5. Explain your reasoning for each measure.
35. Construct the bisector of A. List the steps.
36. Inscribe a regular hexagon in the circle below.
Explain why your construction produces a regular hexagon.
37. Inscribe an equilateral triangle in the circle below.
Explain why your construction produces an equilateral triangle.
38. Inscribe a square in the circle below.
1
. The image of the segment is then
4
dilated with center P and scale factor 2. Find the length of the image segment after each dilation.
39. A segment with length 7 cm is dilated with center O and scale factor
40. Suppose the scale factor of a dilation that maps ABC onto DEF is 3, and suppose BC  7 cm.
What conclusion can you make about a side in DEF? Explain your reasoning.
41. Are JKL and MNO similar? Explain, using similarity
transformations to map JKL onto MNO.
42. Before rock climbing, Michelle wants to know how high she will climb.
She places a mirror on the ground and walks backward until she can
see the top of the cliff in the mirror. She drew a sketch of the situation.
Explain why the triangles formed are similar. Then find the height of the cliff.
43. Andy wants to find the distance across a river. In order to find the
distance CD, Andy stands at point D, directly across from point C, and
walks 200 feet to the left, placing a marker at a point E. Andy continues
walking another 300 feet to point A, and then follows the path to the left,
walking until the markers at points E and C line up. Andy marks this
location B and measures AB.
a. Show that
EAB 
EDC.
b. Use the fact that corresponding sides of similar triangles are proportional to find CD.