given BD and AC bisects each other. prove AB\\ CD
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From step #6, AB is congruent to CD by CPCTC or Corresponding Parts of Congruent Triangles are Congruent.
Triangles ABE and CDE are congruent by SAS postulate.
Therefore, angle B and angle D are congruent.
Note that the segment BD is a transversal line that cuts AB and CD, and angle B and angle D are alternate interior angles.
The answer is :
XY || WZ ⇒ AB || CD
with a reason of :
Parallel lines cut by a transversal form congruent alternate interior angles.