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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.
Solution
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.
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