A pair of opposite sides is both parallel and congruent.To prove that a quadrilateral is a parallelogram, it is enough to show that one of these conditions is satisfied. Now let's analyze the given quadrilateral.
Now, let's think if we can use any of the conditions for parallelograms in this case.
Condition
Can We Use It?
Explanation
Both pairs of opposite sides are parallel.
No *
We have no parallel markers.
Both pairs of opposite sides are congruent.
No *
Only one pair of opposite sides is congruent.
Both pairs of opposite angles are congruent.
No *
We have no information about any angle measure.
The diagonals bisect each other.
No *
We only know that one diagonal is bisected.
A pair of opposite sides is both parallel and congruent.
No *
We have no parallel or congruence markers on any side.
Unfortunately we cannot use any of the conditions. Therefore, it is not necessarily a parallelogram.
