ABCD is a parallelogram.P and Q are mid points of sides AB and CD.Show that PQRS is a parallelogram

  In parellogram ABCD , P and Q are mid point of AB  and CD 

   Join AQ , PD ,  and let the point of intersection be S.

 Join  BQ and PC . let the point of intersection be R.

 To prove PQRS a parellogram,

 AP is = 1/2 Of AB

QC is = 1/2 of CD  ( given P and Q are mid point of AB and CD )

 AP is parellel to CQ ( ABCD is a parellogram )

so APCQ is a parellogram

 similarly we can prove PBQD is a parellogram.

 PR and SQ are part of parellogram

 so PQRS is a parellogram