Question

can the following quadrilateral be proven to be a parallelogram based on the given information? explain.
choose the correct answer below.
a. no. it cannot be proven because the same pair of opposite sides are not congruent and parallel.
b. yes. it can be proven because both pairs of opposite sides are congruent.
c. yes. it can be proven because both pairs of opposite angles are congruent.
d. no. it cannot be proven because at least two of the adjacent angles are not congruent to each other.

Explanation:

Step1: Recall parallelogram properties

One of the parallelogram properties is that if one pair of opposite sides is both congruent and parallel, then the quadrilateral is a parallelogram.

Step2: Analyze the given figure

In the figure, we have one pair of opposite sides marked as parallel (by the red arrows) and another pair of opposite sides marked as congruent (by the red tick - marks). But for the same pair of opposite sides, we don't have both congruence and parallelism information.

Step3: Check each option

• Option B: The figure does not show both pairs of opposite sides are congruent.
• Option C: The figure does not give any information about the angles.
• Option D: Adjacent - angle congruence is not relevant to the parallelogram - determination property we are using (based on side properties here).
• Option A: Since for the same pair of opposite sides, we don't have both congruence and parallelism (which is a valid parallelogram - proving condition), this option is correct.

Answer:

A. No. It cannot be proven because the same pair of opposite sides are not congruent and parallel.