An easier way to remember where to start is to have a diagram....
points A and B are on one line and D and C are on another line and the lines are parallel
Next, connects AD and BC which forms a parallelogram. E is the intersection of the diagonals.
Since alternate and interior angles are congruent and AD = BC because of the parallel lines,
AE = CE and DE = BE because the triangles formed inside the parallelogram are congruent via
at least 2 theorems
The conclusion follows by multiplying the bolded equations above together