Question

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

• A. True
• B. False

Answer 1

The correct option is A True

Given: Parallelogram ABCD, L and M are mid points of $AB$ and $DC$ respectively.
We know,
$AB=CD$
Hence, $DM=LB$ and $DM\parallel LB$ (As, $AB\parallel CD$)
Suppose $DL$ and $MB$ intersect AC at P and Q respectively.
Consider, $△ABC$,
$PL\parallel QB$
L is mid point of $AB$
Hence, P is mid point of AQ (Converse of mid point theorem)
Thus, $AP=PQ$ (1)
Similarly, in $△CDP$
$CQ=QP$ (2)
From (1) and (2)
$AP=PQ=CQ$
Hence, P and Q trisect diagonal $AC$