Question

L and M are the mid-point of sides AB and DC respectively of parallelogram ABCD. Prove that segments DL and BM trisect diagonal AC.

Answer 1

The required figure is shown below

From figure,

BL = DM and BL || DM and BLMD is a parallelogram, therefore BM || DL

From triangle ABY

L is the midpoint of AB and XL || BY, therefore x is the midpoint of AY.ie AX = XY                                    …..(1)

Similarly for triangle CDX
CY=XY                                                …..(2)

From (1) and (2)
AX = XY = CY and AC = AX + XY + CY
Hence proved.