The coordinates of parallelogram abcd are a(0, 0) , b(a, 0) , c(
,
), and d(c, b) .

the coordinates of the midpoint of ac are (
, b2 ).

the coordinates of the midpoint of bd are ( a+c2 ,
).

the midpoints of the diagonals have the same coordinates.

therefore, ac and bd bisect each other.