Question

does the fact that yz = wx lead to the proof that xywz is a parallelogram? why or why not?
a yes; all angles will be right angles, and so the sides are parallel
b no; both pairs of opposite sides can be congruent without being parallel.
c yes; if both pairs of opposite sides are congruent, they must also be parallel
d no, opposite angles may not be equal.

Explanation:

To determine if \( YZ = WX \) (along with the marked congruent sides \( XY = WZ \) from the diagram) proves \( XYWZ \) is a parallelogram, we recall the parallelogram theorem: A quadrilateral is a parallelogram if both pairs of opposite sides are congruent (and thus parallel). Here, we have \( XY = WZ \) (marked) and \( YZ = WX \) (given). By the theorem, if both pairs of opposite sides are congruent, they must also be parallel, satisfying the parallelogram definition. Option A is incorrect (no info about right angles), B is wrong (the theorem says congruent opposite sides imply parallel), D is irrelevant (angle equality isn’t the focus here).

Answer:

C. Yes; if both pairs of opposite sides are congruent, they must also be parallel