a.
To find:The statement “A quadrilateral is a parallelogram ifdiagonals are congruent” is always, sometimes or never true.
a.

Answer to Problem 11PSB
The statement issometimes true.
Explanation of Solution
Given information:
A parallelogram OJKM with diagonals OK and JM.
The below property is used:
The diagonals of a parallelogram are sometimes congruent.
b.
To find: The statement “A quadrilateral is a parallelogram if one pair of opposite sides are congruent and one pair of opposite sides are parallel” is always, sometimes or never true.
b.

Answer to Problem 11PSB
The statement is sometimes true.
Explanation of Solution
Given information:
A parallelogram OJKM with diagonals OK and JM.
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
The below property is used:
If a quadrilateral has two sets of opposite sides congruent, then it is a parallelogram.
c.
To find: The statement “A quadrilateral is a parallelogram if each pair of consecutive
c.

Answer to Problem 11PSB
The statement is always true.
Explanation of Solution
Given information:
A parallelogram ABCDwith diagonals AC and BD.
Angle BAD is congruent to angle GCB.
Angle GBC and angle CBA are supplementary.
Angle BAD and angle CBA are supplementary.
d.
To find: The statement “A quadrilateral is a parallelogram if all angles are right angles” is always, sometimes or never true.
d.

Answer to Problem 11PSB
The statement is always true.
Explanation of Solution
Given information:
A parallelogram PQRSwith diagonals PR and QS.
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
The below property is used:
A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides.
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