Question

given the information marked on the figures below, classify each quadrilateral as a \parallelogram\ or
ot necessarily a parallelogram.\ note that each figure is drawn like a parallelogram, but you should not rely on how the figure is drawn in determining your answers. if necessary, you may learn what the markings on a figure indicate.

Explanation:

Step1: Analyze the first figure (top - left)

In the first figure, we have two pairs of parallel sides (indicated by the arrows). But for a parallelogram, we need both pairs of opposite sides to be parallel. Here, we only know about two sides being parallel. So it is not necessarily a parallelogram.

Step2: Analyze the second figure (top - right)

In the second figure, we have one pair of parallel sides (indicated by the arrows) and one pair of equal sides (indicated by the tick - marks). But this is not sufficient to prove it is a parallelogram. So it is not necessarily a parallelogram.

Step3: Analyze the third figure (bottom - left)

In the third figure, we have four angles. But having four angles is not a sufficient condition for a parallelogram. So it is not necessarily a parallelogram.

Step4: Analyze the fourth figure (bottom - right)

In the fourth figure, the diagonals bisect each other (indicated by the tick - marks on the diagonals). One of the properties of a parallelogram is that its diagonals bisect each other. So this figure is a parallelogram.

Answer:

First figure: Not necessarily a parallelogram
Second figure: Not necessarily a parallelogram
Third figure: Not necessarily a parallelogram
Fourth figure: Parallelogram