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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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