Complete the coordinate proof of the theorem.

given: abcd is a parallelogram.

prove: the diagonals of abcd bisect each other.

parallelogram in quadrant 1 of the coordinate plane with vertices at a begin ordered pair 0 comma 0 end ordered pair, b begin ordered pair a comma 0 end ordered pair, c begin ordered pair a plus c comma b end ordered pair and d.

enter your answers in the boxes.

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

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

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

the midpoints of the diagonals have the same coordinates.

therefore, the diagonals of abcd bisect each other.