1.

The diagonals of a quadrilateral `A B C D`are perpendicular. Show that the quadrilateral, formed by joining themid-points of its sides, is a rectangle.

Answer» To prove-PQRS is a rectangle
Proof-
`In /_ABC`,PQ||AC and PQ=1/2AC
`In /_ADC` SR||AC and SR=1/2AC
In PQRS PQ=SR,PQRS is a parallelogram
PS||BO and PN||NO
PQ||AC and PM||QN
PMON is a parallelogram
`/_MPN=/_MON`
`/_MPN=90^@`
`/_MPN=/_QPS=90^@`
PQRS is a rectangle.


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