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ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

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ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.
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`AB=CD`
`AD=BC`
`AP=PB=1/2*AB`
`DR= RC = 1/2*DC`
`AP=PB=RD=RC`
`AS=SD=BQ=CQ`
`/_ APS, /_ SDR`
`AS-SD`
`AP=RD`
`/_D= /_A`
`SP=SR`
`PQ=QR`
`SP=PQ`
`:. SP=PQ=QR=RS`
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