Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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If two polygons are SIMILAR, then the corresponding sides must be _____.
a. | proportional | c. | parallel | b. | congruent | d. | similar |
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2.
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Given that  solve for x and y. 
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3.
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Use the Angle-Angle Similarity Theorem to determine which pair of triangles is
not similar.
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4.
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The triangles formed by two ladders leaning against a wall are similar. How far
up the wall does the shorter ladder reach?  a. | 28 ft | b. | 14 ft | c. | 12 ft | d. | 10
ft |
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5.
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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?  a. | 31.725 ft | b. | 42.3 ft | c. | 47.9
ft | d. | 56.4 ft |
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6.
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Which of the following proportions could be used as a given to show that  ? 
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7.
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Given the directed line segment from A to B, construct a point
P that divides the segment in the ratio 4 to 1 from A to B.
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Short Answer
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8.
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In the diagram, PQRS  WXYZ, find the values of
x, y, and z.
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9.
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Are the two triangles (not drawn to scale) similar? If so, explain why they
are.  
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10.
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Are all regular pentagons similar? Explain.
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11.
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 is the dilation of 
with scale factor 3. Find the proportions  and  .
Justify your work. 
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12.
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Which triangle is not similar to any of the others? 
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13.
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True or false: triangle CDE is similar to triangle
FGH.  
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14.
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 ,  , and  .
Explain how you can prove that  . 
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15.
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Explain why the triangles are similar and write a similarity
statement. 
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16.
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What value of x will make the two triangles similar? 
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17.
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Determine whether the triangles are similar. If they are similar, write a
similarity statement.
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Problem
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18.
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Complete the proof of the AA Similarity Theorem.  Given:  ;  Prove:  Find a sequence of similarity transformations that maps 
onto  . a. Apply a dilation to 
with scale factor  . Let the image of  be  .  is similar to  because a dilation is a similarity transformation. Also,  and  because _____________________________. b.  . c. It is
given that  and  . By the Transitive Property of Congruence,  and  . d.  by  . This means there is a sequence of rigid motions that maps  onto  . The dilation in step a followed by this
sequence of rigid motions maps  onto  . So,  .
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19.
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In the figure below,  ,  ,
and  . List all the angles in the figure that are
congruent to  and justify your answer. Find one other angle
in  that corresponds to a congruent angle in the
other triangles. Then find similarity transformations that map  onto  ,  onto  , and  onto  . 
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20.
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Given:  Prove:   a. First, show that
 . Take the
reciprocal of both sides of the given proportion to obtain _______.
Add  to the left side and 
to the right side to obtain  . This is valid because both fractions are
equivalent to ____. Use the Segment Addition Postulate to rewrite
 as _______.
Because  ,  by
____________. b. Use the properties of similar triangles to show
that  .  ______ because corresponding angles in similar triangles are
congruent. So,  because
____________________________.
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