Question

Given BD and AC bisects each other. prove AB\\ CD

Answer 1

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.