Please answer the foll:question

Asked by ashwati | 8th Mar, 2009, 06:05: PM

Expert Answer:

DM=LB  (both are half of equal sides AB and CD)

 and

 DM paralle to LB (as AB and CD are parallel)

So, DLBM is a parallelogram.(one pair of opposite sides is parallel and equal)

So we get, DL parallel  to MB.

Suppose DL and BM intersect AC in P and Q respectively.

Consider triangle ABC,

PL  parallel to QB ( as DL parallel to MB)

L is the midpoint of AB,

 so P must be the mid point of AQ( conv of mid pt thm)

So,

 AP=PQ..(i)

Simly, considering triangle CDP,

we get

CQ=QP..(ii)

from (i) and (ii), we get,

AP=PQ=CQ.

Thus,

 P and Q trisect the diagonal AC.

Answered by  | 8th Mar, 2009, 10:32: PM

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