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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.

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ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that : (i) S R || A C and S R=1/2A C (ii) P Q = S R (iii) PQRS is a parallelogram

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

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A B C D is a quadrilateral; P , Q , Ra n dS are the points of trisection of side A B ,B C ,C Da n dD A respectively and are adjacent to Aa n dC ; prove that P Q R S is parallelogram.

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RD SHARMA ENGLISH-QUADRILATERALS-All Questions
  1. ABCD is a rhombus and P ,Q ,R ,S are the mid-points of A B ,B C ,C D ,...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. 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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  19. Prove that In a parallelogram, opposite side are equal

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  20. The opposite angles of a parallelogram are equal.

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