Question

based on the information given, is the quadrilateral a parallelogram? explain. the figure is a parallelogram because there are two pairs of congruent sides. the figure is a parallelogram because a diagonal is bisected. the figure is not necessarily a parallelogram because the diagonals are not congruent. the figure is not necessarily a parallelogram because only one diagonal is bisected and only one pair of sides is congruent.

Explanation:

Step1: Recall parallelogram properties

One - of the properties of a parallelogram is that both pairs of opposite sides are congruent, both pairs of opposite angles are congruent, and the diagonals bisect each other. In the given figure, we see that only one diagonal is bisected and only one pair of sides is marked as congruent.

Step2: Analyze the options

• Option 1: Having two pairs of congruent sides is a property of a parallelogram, but the figure does not show two pairs of congruent sides.
• Option 2: A diagonal being bisected is not enough to prove a figure is a parallelogram. Both diagonals should bisect each other.
• Option 3: Diagonal congruence is not a necessary condition for a figure to be a parallelogram.
• Option 4: Since only one diagonal is bisected and only one pair of sides is congruent, the figure is not necessarily a parallelogram.

Answer:

The figure is not necessarily a parallelogram because only one diagonal is bisected and only one pair of sides is congruent.