Questions

1) Fill in the blank. A quadrilateral is a __________ with four sides.

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2) The shape is a quadrilateral.

True

False

3) The shape is a quadrilateral.

True

False

4) The shape is a quadrilateral.

True

False

5) The shape is a quadrilateral.

True

False

6) A parallelogram is a quadrilateral with opposite sides that are _________.

a.) parallel

b.) perpendicular

c.) intersecting

d.) skew

7) Which theorem is depicted by the figure and information shown below?

a.) Opposite sides of parallelograms are congruent. (Tm. 14-A)

b.) Opposite angles in a parallelogram are congruent. (Tm. 14-B)

c.) The sum of any two consecutive angles within a parallelogram equals 180. (Tm. 14-C)

d.) The diagonals of a parallelogram bisect each other. (Tm. 14-D)

e.) The diagonal of a parallelogram separates it into two congruent triangles. (Tm. 14-E)

8) Which theorem is depicted by the figure and information shown below?

a.) Opposite sides of parallelograms are congruent. (Tm. 14-A)

b.) Opposite angles in a parallelogram are congruent. (Tm. 14-B)

c.) The sum of any two consecutive angles within a parallelogram equals 180. (Tm. 14-C)

d.) The diagonals of a parallelogram bisect each other. (Tm. 14-D)

e.) The diagonal of a parallelogram separates it into two congruent triangles. (Tm. 14-E)

9) Which theorem is depicted by the figure and information shown below?

a.) Opposite sides of parallelograms are congruent. (Tm. 14-A)

b.) Opposite angles in a parallelogram are congruent. (Tm. 14-B)

c.) The sum of any two consecutive angles within a parallelogram equals 180. (Tm. 14-C)

d.) The diagonals of a parallelogram bisect each other. (Tm. 14-D)

e.) The diagonal of a parallelogram separates it into two congruent triangles. (Tm. 14-E)

10) Which theorem is depicted by the figure and information shown below?

a.) Opposite sides of parallelograms are congruent. (Tm. 14-A)

b.) Opposite angles in a parallelogram are congruent. (Tm. 14-B)

c.) The sum of any two consecutive angles within a parallelogram equals 180. (Tm. 14-C)

d.) The diagonals of a parallelogram bisect each other. (Tm. 14-D)

e.) The diagonal of a parallelogram separates it into two congruent triangles. (Tm. 14-E)

11) Which theorem is depicted by the figure and information shown below?

a.) Opposite sides of parallelograms are congruent. (Tm. 14-A)

b.) Opposite angles in a parallelogram are congruent. (Tm. 14-B)

c.) The sum of any two consecutive angles within a parallelogram equals 180. (Tm. 14-C)

d.) The diagonals of a parallelogram bisect each other. (Tm. 14-D)

e.) The diagonal of a parallelogram separates it into two congruent triangles. (Tm. 14-E)

12) Name the coordinates of point T that when placed in Quadrant II makes parallelogram QRST.

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13) Name the coordinates of point T that when placed in Quadrant IV makes parallelogram QRTS.

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14) Determine if quadrilateral DEFG, with vertices D(–4,2), E(2,5), F(3,0) and G(–1,–2), is a parallelogram. State your answer and support it by giving an explanation based on the slopes of the sides of the quadrilateral.

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15) Find the value of “x”.

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16) Find the value of “x”.

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17) Find the value of “x”.

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18) Find the value of “x”.

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19) Refer to the parallelogram and information given below to answer the following questions: (a) What is the measure of angle 1? (b) What is the measure of angle 2? (c) What is the measure of angle 3? (d) What is the measure of angle 4?

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20) For parallelogram LMNP, write an expression to represent the length of segment LN if the length of segment RN equals “9x”.

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21) In parallelogram JKLM diagonals JL and KM intersect at point Q. IF KQ = x – 13 and MQ = 2x – 43, answer the following questions: (a) What is the value of “x”? (b) What is the length of diagonal KM?

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22) In parallelogram ABCD, the measurement of angle A equals “7x + 22” and the measure of angle B equals “2x – 13”. What is the measure of each of the four angles in the parallelogram?

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23) Answer the following: (a) What is the measure of angle S? (b) What is the measure of angle R? (c) What is the measure of angle T?

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24) Answer the following: (a) What is the measure of angle BCD? (b) What is the measure of angle ABC? (c) What is the measure of angle ADC?

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25) Answer the following: (a) What is the measure of angle SDC? (b) What is the measure of angle TDA? (c) What is the measure of angle TAD?

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26) Answer the following: (a) What is the measure of angle QAB? (b) What is the measure of angle QBA? (c) What is the measure of angle RBC? (d) What is the measure of angle BCR?

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27) What is the missing part of the ordered pair for point J?

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28) What is the missing part of the ordered pair for point K?

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29) Fill in the blank. Theorem 14-F: In a quadrilateral if both pairs of __________ are congruent, then the quadrilateral is a parallelogram.

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30) Fill in the blank. Theorem 14-G: In a quadrilateral if both pairs of __________ are congruent, then the quadrilateral is a parallelogram.

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31) Fill in the blank. Theorem 14-H: In a quadrilateral if its diagonals __________ each other, then the quadrilateral is a parallelogram.

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32) Determine values for x and y, so that quadrilateral ABCD is a parallelogram.

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33) Fill in the blank. Theorem 14-I: In a quadrilateral if one pair of opposite sides is both __________, then the quadrilateral is a parallelogram.

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34) A rectangle is a parallelogram with four __________.

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35) Refer to rectangle LMNP shown below to answer the following questions: (a) What are the coordinates of point P? (b) What are the coordinates of point M?

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36) Given that angle KGL is complementary with angle GLK, then the measures of the two angles must total __________ degrees, and by the Triangle Sum Theorem, angle K must equal __________ degrees.

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37) Since angle K and angle KGH are consecutive interior angles of parallel lines GH and KL, then their sum equals __________ and the measure of angle KGH equals __________ degrees.

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38) Since angle K and angle KLH are consecutive interior angles of parallel lines ____ and ____, their sum equals 180 degrees and the measure of angle KLH equals 90 degrees.

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39) Since angle K and H are opposite angles of a parallelogram, angle H must equal __________ degrees.

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40) Thus, each of the four angles in parallelogram GHLK equals __________ degrees, and by definition, the parallelogram is a __________.

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41) Fill in the blank. Theorem 14-J: If a parallelogram is a rectangle, then its __________ are congruent.

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42) Refer to rectangle ABCD and the information below to answer the following questions: (a) What is the value of “x”? (b) What are the lengths of segments AC and BD?

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43) Fill in the blank. Theorem 14-K: If the diagonals of a parallelogram are congruent, then the parallelogram is a __________.

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44) The consecutive angles are supplementary.

a.) true for parallelograms only

b.) true for rectangles only

c.) true for both parallelograms and rectangles

45) The diagonals bisect each other.

a.) true for parallelograms only

b.) true for rectangles only

c.) true for both parallelograms and rectangles

46) The diagonals are congruent.

a.) true for parallelograms only

b.) true for rectangles only

c.) true for both parallelograms and rectangles

47) All four angles are right angles.

a.) true for parallelograms only

b.) true for rectangles only

c.) true for both parallelograms and rectangles

48) All properties that apply to a parallelogram also apply to a rectangle.

True

False

49) All properties of a rectangle also apply to a parallelogram.

True

False

50) Write a proof for the given information and the conclusion. You may write the proof in paragraph form or you may write a formal proof using statements and reasons. If you write a formal proof, you may complete the proof in a word-processing document and attach it below.

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