Question

Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given XY = WZ and XW = YZ
a.

No; you cannot determine that the quadrilateral is a parallelogram.


b.

Yes; two opposite sides are both parallel and congruent.


c.

Yes; opposite sides are congruent.


d.

Yes; diagonals of a parallelogram bisect each other.

Answer 1

The best answer is Letter C - Yes, opposite sides are congruent.

If both pairs of opposite sides of a quadrilateral are congruent, then you'll always have two opposite pairs of parallel sides. Congruent means that they measure the same. Since two congruent sides separating the other pair of opposite sides must always keep those opposite lines the same distance apart, then, the opposite sides are also parallel.