Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Given  , Miguel is proving  .
He has drawn auxiliary line l, parallel to  . Which of the following
congruencies is likely to be part of his proof? 
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2.
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If  , which segment is congruent to  ?
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3.
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The figure shows the paths through a park. Which justifies the statement  ? 
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4.
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What additional information will prove  by
HL?  a. |  | b. |  |
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5.
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If  and  are right
angles,  , and  , which
theorem proves  ? 
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6.
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Kartik is proving that the base angles of an isosceles triangle are congruent.
He begins with the illustration of isosceles  below.  By definition,  and by the Reflexive Property,  . He then asserts  and  because
corresponding parts of congruent triangles are congruent. Why is  ?
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7.
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Refer to the figure shown. Which of the following statements is true? 
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8.
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 . Name the theorem that justifies the
congruence. 
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9.
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Which conclusion can be drawn from the given facts in the diagram? 
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10.
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A right triangle with leg lengths of a and b units has to be
positioned in the coordinate plane to write a coordinate proof. Which set of coordinates is
convenient for finding the length of the hypotenuse?
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11.
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Which of the following would you find most useful in giving a coordinate proof
that two triangles are congruent by SSS?
a. | Distance Formula | b. | Midpoint Formula | c. | Corresponding parts
of congruent triangles are congruent. | d. | Slope Formula |
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12.
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 has vertices A(0, 10), B(8,
11), and C(6, 3). Which coordinate proof correctly shows that  is a scalene
triangle?
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Short Answer
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13.
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In the figure below,  . Find  . 
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14.
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For the two triangles shown,  ,  ,
and  .  From the
given information, must there be a sequence of rigid transformations that maps 
to a segment in  ? What segment corresponds to  ?
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15.
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 . Name the theorem that justifies the
congruence. 
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16.
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Prove that A(1, 1), B(3, 3), and C(5, 1) are the vertices
of a right triangle.
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17.
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Consider  with vertices  ,  , and   a. Prove or disprove that 
is isosceles. b. Use the result from part a to prove or disprove
that  is equilateral.
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