Exercise 12 Page 418

Let's begin by reviewing the conditions for parallelograms.

• Both pairs of opposite sides are parallel.
• Both pairs of opposite sides are congruent.
• Both pairs of opposite angles are congruent.
• The diagonals bisect each other.
• A pair of opposite sides is both parallel and congruent.

To prove that a quadrilateral is a parallelogram, it is enough to show that one of these conditions is satisfied. Now let's analyze the given quadrilateral.

Now, let's think if we can use any of the conditions for parallelograms in this case.

Unfortunately we cannot use any of the conditions. Therefore, it is not necessarily a parallelogram.