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The diagonals of a quadrilateral A B C D...

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

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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
...
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RD SHARMA-QUADRILATERALS-All Questions
  1. If diagonal of a parallelogram bisects one of the angles of the par...

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  2. Show that the quadrilateral, formed by joining the mid-points of the ...

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  3. The diagonals of a quadrilateral A B C D are perpendicular. Show that ...

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  4. ABCD is a rhombus and P ,Q ,R ,S are the mid-points of A B ,B C ,C D ,...

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  5. Show that the quadrilateral formed by joining the mid-points of the ...

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  6. Prove that the figure formed by joining the mid-points of the pair of ...

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  7. In Figure, A D is the median and D E A Bdot Prove that B E is the med...

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  8. In a A B C , find the measures of the angles of the triangle formed b...

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  9. In A B C ,A D is the median through A and E is the mid-point of A D ....

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  10. In Figure, A D , and B E are medians of A B C and B E || D Fdot Prove...

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  11. P ,Q and R are, respectively, the mid-points of sides B C ,C A and A B...

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  12. P is the mid-point of side A B of a parallelogram A B C D . A Line thr...

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  13. In Figure, A B C D isa trapezium in which side A B is a parallel to si...

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  14. In Figure, A B C D is a parallelogram. E and F are the mid-points of t...

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  15. A B C D is a parallelogram. P is a point on A D such that A P=1/3A D a...

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  16. In a A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a n d\ C r...

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  17. In triangle ABC, M ,N and P are the mid-points of A B ,A C and B C res...

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  18. Prove that the line segment joining the mid-points of the diagonals of...

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  19. In a triangle A B C median A D is produced to X such that A D=D Xdot P...

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  20. In Delta ABC the lines are drawn parallel to BC,CA and AB respectively...

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