Question

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

Explanation:

To determine if a quadrilateral is a parallelogram, there are several criteria. One of the key theorems is that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Another is that if both pairs of opposite sides are congruent, or if one pair of opposite sides is both parallel and congruent, the quadrilateral is a parallelogram.
In the first statement, only one diagonal is bisected and only one pair of sides is congruent. This does not meet any of the parallelogram - determining criteria. For example, a quadrilateral with one pair of congruent sides and one bisected diagonal could be a non - parallelogram (like a kite - like shape in some cases).
For the second statement, the congruence of diagonals is a property of rectangles (a special type of parallelogram), but not a general property for all parallelograms. A parallelogram does not require its diagonals to be congruent. However, the main issue is that the first statement correctly identifies the lack of sufficient conditions (based on the given information in the figure, assuming the markings correspond to one bisected diagonal and one pair of congruent sides) rather than the non - congruence of diagonals (which is not a necessary condition for a general parallelogram).

Answer:

The first explanation (The figure is not necessarily a parallelogram because only one diagonal is bisected and only one pair of sides is congruent) is the correct reason.