Please answer the foll:question
Construction : Draw a line PR parallel to CD , R lies on AD.
From corollary to mid point theoram in triangle ADC , as PR|| CD, P being the mid point , R is the mid point of AD.
As CD||AB, we have PR|| CD..Consider the triangle ABC, we have R as mid point of AD and similar as above it meets BD at midpoint i.e Q. Thus PQ||AB.
Now applying midpoint theoram in triangle ADC, RP=1/2 CD
and applying the midpoint theoram in ABD,RQ=1/2 AB
So we have , PQ=RP-RQ=1/2 (CD-AB)
Note: Above solution assumes that CD is the larger side.
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