Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What is the measure of  ? 
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2.
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Which circle is inscribed in a triangle?  a. | Circle X | b. | Circle Y | c. | Circle
Z | d. | None of the circles is inscribed in a triangle. |
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3.
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Which of the following best describes how to find the circumcenter of a
triangle?
a. | Find the intersection of the three altitudes of the triangle. | b. | Find the
intersection of the perpendicular bisectors of the sides of the triangle. | c. | Find the
intersection of the angle bisectors for each angle in the triangle. | d. | Find the
intersection of the three medians of the triangle. |
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4.
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Which statement can you make about the triangle?
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5.
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List the angles of  in order from smallest to largest.
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6.
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List the sides of  in order from shortest to longest.
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7.
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What theorem justifies the statement WX >
ST? a. | Hinge Theorem | c. | Triangle Longer Side Theorem | b. | Converse of the
Hinge Theorem | d. | Triangle
Inequality Theorem |
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Short Answer
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8.
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Use the figure below to prove that the segment connecting the midpoints of two
sides of a triangle is parallel to the third side and has a length that is half that of the third
side. 
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9.
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Describe the possible lengths of the third side of a triangle given the lengths
of the other two sides are 8 centimeters and 10 centimeters.
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Essay
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10.
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 is equilateral, and D is the
incenter. Part A: Prove    . Part B: What can you
conclude about the incenter and the circumcenter of  ? Justify your
reasoning. 
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11.
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 is both an altitude and a median of  .  Explain why  must be
isosceles.
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12.
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 and  are medians
to the legs of isosceles triangle  .  Samir is
going to prove  . He knows that  because they
are the base angles of an isosceles triangle. He asserts  ,  ,
and then states that  and  must be
congruent because they are corresponding parts of congruent triangles. Explain how Samir knows
that  .
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13.
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Maggie used this figure in a coordinate proof showing that the median from the
vertex angle of an isosceles triangle is also an altitude of that triangle. What must be true about
 to be an altitude of the isosceles
triangle? Show that  is an altitude. 
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14.
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Use the given information and the figure to answer the
question. Given:  is a midsegment of  . 
Find  .
Justify your answer.
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15.
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Describe the important elements of a coordinate proof and an indirect proof.
Give examples of each kind of proof.
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16.
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Stephan is using  to prove the Triangle Inequality
Theorem.  He begins by adding point J so that
 , creating isosceles triangle
MJL. By the Segment Addition Postulate
NJ = NL + JL, and by construction,  is smaller than  . Stephan claims this makes  smaller than  , and because the larger angle in a triangle is across from the larger side, NM
< JN. So, by substitution NM < NL + JL. Because this process can
be repeated using any of the three sides to create the isosceles triangle, every side is smaller than
the sum of the lengths of the other 2 sides. In Stephan’s proof, he claims  is smaller than  . Explain why this must be true.
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