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 sum of the measures of the interior angles of a
pentagon?
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2.
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Which of the following is a valid conclusion given parallelogram 
with diagonals  and  ? a. |  | c. |  | b. |  and  are
supplementary. | d. |  |
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3.
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Which information is sufficient to prove that quadrilateral ABCD is a
parallelogram?
a. | The diagonals bisect each other. | c. |  and  are supplementary. | b. |  | d. |  |
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4.
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Given  and  , what
triangle congruence theorem is likely to be used in a proof that  and
 ?  Given:
 and  Prove:
 and 
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5.
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Show that GHIJ is a parallelogram for x = 5 and y =
8.  Complete the
explanation.
 |  | Given |  [1] | GJ = 7(5) 20 = [2] | Substitute and simplify. | | | | |  |  | Given |  [3] |  [4] | Substitute and simplify. | | | |
Because HI =
GJ and GH = JI, GHIJ is a parallelogram because [5]. a. | [1] 15
[2] 15
[3] 24
[4]
24
[5] both sets of opposite sides are congruent.
| b. | [1]
15
[2] 24
[3] 15
[4] 24
[5] one set of opposite
sides is parallel and congruent.
| c. | [1] 15
[2]
15
[3] 24
[4] 24
[5] both sets of opposite sides are
parallel.
| d. | [1] 24
[2] 24
[3] 15
[4]
15
[5] both sets of opposite angles are congruent.
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6.
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Choose the statement with the correct reasoning in the proof below.  Given:  ;  Prove: 
is a parallelogram. Statements | Reasoning | 1.  ;  | 1. Given | 2.  ;  | 2. [?] | 3.   | 3. SAS Congruence Theorem | 4.  ;  | 4. Corresponding parts of congruent triangles are
congruent. | 5.  is a parallelogram. | 5. If both pairs of opposite sides are congruent, a quadrilateral is a
parallelogram. | | |
a. | If a quadrilateral is a parallelogram, opposite angles are
congruent. | b. | Reflexive Property of Congruence | c. | When parallel lines are cut by a transversal,
alternate interior angles are congruent. | d. | Vertical angles are
congruent. |
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7.
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Choose the correct statement in the proof below. Given: 
is a kite,  , and  Prove:
 Statements | Reasoning | | 1. Given | 2. B and D lie on the 
bisector of  . | 2. Converse of the  Bisector
Theorem | 3. [?] | 3. Through any two points,
there exists exactly one line. | 4.  | 4. Definition of 
bisector | | |
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Short Answer
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8.
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Decide if you are given enough information to prove that the quadrilateral is a
parallelogram: One pair of opposite sides are congruent.
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9.
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Decide if you are given enough information to prove that the quadrilateral is a
parallelogram: Diagonals are perpendicular.
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10.
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Decide if you are given enough information to prove that the quadrilateral is a
parallelogram: Diagonals are perpendicular and congruent.
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11.
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Show that JKLM is a parallelogram for  and  . 
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12.
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 and  . Is
PQRS a parallelogram? Explain. 
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13.
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Jermaine wants to prove that the diagonals of rectangle 
are congruent. He plans to use the SSS Congruence Theorem to conclude that  .
Do you agree with his plan? Explain. 
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Problem
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14.
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Find the measure of each of the numbered angles.
Explain your reasoning for each angle. 
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Essay
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15.
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Given:  and  Prove:
 is a parallelogram. 
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16.
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Write an indirect proof to show that one diagonal of a trapezoid cannot bisect
the other. That is, show that in the diagram, it cannot be true that  bisects  in trapezoid ABCD. 
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