ABCD is a parallelogram .

Asked by  | 6th Dec, 2008, 11:54: AM

Expert Answer:

Construction : Join the diagonal BD.

In triangle ABD,

use mid point theorem to prove that, PS parallel to QR.

Similarly,show that PQ is parallel to SR by joining the diagonal AC.

Thus, PQRS is a parallelogram.

Hence PQ=RS, as they are opposite sides of  the  parallelogram PQRS.

Alternately, use the property that line segment joining the midpoints of two sides of a triangle is parallel to the third side and also half of it.In this case , you will need to consider only one of the diagonals  i.e. AC.

Show PQ=1/2(AC) and also SR=1/2(AC),.So they become equal.

 

Answered by  | 6th Dec, 2008, 12:58: PM

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