ABCD is a quadrilateral in which ab is equal to BC if P Q R S be the midpoint of Ab BC CD and BD respectively so that pqrs is a rh

1 thought on “ABCD is a quadrilateral in which ab is equal to BC if P Q R S be the midpoint of Ab BC CD and BD respectively so that pqrs is a rh”

1. In △BAD, P and S are mid-points of AB and BD

   ⇒ PS∥AD and PS=

   2

   1

   AD — ( 1 ) [ By BPT ]

   Similarly in △CAD,

   ⇒ OR∥AD and QR=

   2

   1

   AD — ( 2 )

   From ( 1 ) and ( 2 ), we get

   ⇒ PS∥QR and PS=QR=

   2

   1

   AD —— ( 3 )

   In △BDC, we get

   ⇒ SR∥BC and SR=

   2

   1

   BC —– ( 4)

   And in △ABC

   PQ∥BC and PQ=

   2

   1

   BC —— ( 5 )

   ⇒ PQ∥SR, PQ=SR=

   2

   1

   BC —- ( 6 ) [ From ( 4 ) and ( 5 ) ]

   ∴ □PQRS is a parallelogram.

   Now, AD=BC

   ∴

   2

   1

   AD=

   2

   1

   BC

   ∴ PS=QR=PQ=SR [ From ( 3 ) and ( 6 ) ]

   ∴ □PQRS is a rhombus.

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