Question

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

Explanation:

Step1: Recall parallelogram properties

One of the properties of a parallelogram is that both pairs of opposite sides are congruent.

Step2: Analyze the given figure

In the given quadrilateral, the markings show that one pair of opposite sides are parallel (indicated by the arrows) and another pair of opposite sides are congruent (indicated by the tick - marks). But the key property here is that for a quadrilateral, if both pairs of opposite sides are congruent, then it is a parallelogram.

• Option A is wrong because there is no information about angles in the figure.
• Option C is wrong because angle congruence (or lack thereof) of adjacent angles is not relevant to the given side - based information.
• Option D is wrong because the figure shows that one pair of sides is parallel and another pair is congruent, but the property of a parallelogram that both pairs of opposite sides are congruent (which is satisfied here) is the correct one.

Answer:

B. Yes. It can be proven because both pairs of opposite sides are congruent.