In parallelogram ABCD, the diagonals meet at point E. Find the lengths of the segments AC and DE, if AE is 7mm, BE is 8mm.

A parallelogram is a geometric figure in which opposite sides are parallel to each other, and its diagonals are halved at their intersection. Let AB side be parallel to DC side and BC side parallel to AD side. The diagonals of the parallelogram are AC and BD, which intersect at point E. By the condition of the problem, AE is equal to 7mm. and BE is 8 mm. Then AE is equal to CE and BE is equal to DE. The length of the required diagonal AC consists of the lengths of the segments AE and CE.
AC = AE + CE = 7 + 7 = 14 (mm).
The length of the segment DE is equal to the length of the segment AE.
DE = AE = 8 (mm).
Answer. The AC diagonal is 14 mm long and the DE length is 8 mm.