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Show that the quadrilateral formed by jo...

Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus.

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Verified by Experts

In `/_\ abc, p & q are mid points of ab and bc`
`pq || ac & pq= (ac)/2`
in `/_\adc, s&r mid point of ad & cd`
`sr || ac & sr = (ac)/2 `
so,`pq || sr , pq=sr `
pqsr is a 11gm
abcd is a rectangle
`ad = bc`
...
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Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR ABC D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

RD SHARMA ENGLISH-QUADRILATERALS-All Questions
  1. The diagonals of a quadrilateral A B C D are perpendicular. Show that ...

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

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

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

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

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

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

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  8. In Figure, A D , and B E are medians of A B C and B E || D Fdot P...

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

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

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

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

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  13. 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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  14. In a triangle A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a...

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  15. In Figure, M ,N and P are the mid-points of A B ,A C and B C respectiv...

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

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

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

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  19. A B C D is a kite having A B=A D and B C=C D . Prove that the figure f...

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  20. Prove that In a parallelogram, opposite side are equal

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