Question

Find AE in the parallelogram, if BD = 12, and AC = 18

Answer 1

See the picture in the attached figure

we know that

There are six important properties of parallelograms to know:

1) Opposite sides are congruent (AB = DC).
2) Opposite angels are congruent (D = B).
3) Consecutive angles are supplementary (A + D = 180°).
4) If one angle is right, then all angles are right.
5) The diagonals of a parallelogram bisect each other.
6) Each diagonal of a parallelogram separates it into two congruent triangles.

so
if the diagonals of a parallelogram bisect each other
then 
AE=EC
AC=AE+EC------> AC=2*AE----> AE=AC/2----> AE=18/2----> AE=9 units

the answer is
AE=9 units