The lengths of the diagonals in a parallelogram can be computed using the law of cosines for the constructed triangle including the sides and and the angle or .
The diagonal , from the upper left corner to the lower right corner of the parallelogram, uses therefore the following formulaThe other diagonal , from the lower left corner to the upper right corner of the parallelogram, includes in the constructed triangle the angle . The angles in a parallelogram have the property thatSo we get the following formula for computing the length of the diagonal
Both diagonals intersect at half of their length, i.e. they bisect each other.