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A quadrilateral A B C D is such that dia...

A quadrilateral `A B C D` is such that diagonal `B D` divides its area in two equal parts. Prove that `B D` bisects `A C`. GIVEN : A quadrilateral `A B C D` in which diagonal `B D` bisects it. i.e. `a r(triangle A B D)=a r(triangle B D C)` CONSTRUCTION : Join `A C` Suppose `A C` and `B D` intersect at `O` . Draw `A M_|_B D` and `C N _|_ B D`. TO PROVE : `A O=O C`.

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RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
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  2. Prove that the area of a rhombus is equal to half the rectangle cont...

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  3. A quadrilateral A B C D is such that diagonal B D divides its area in ...

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  4. Prove that two triangles having the same base and equal areas lie betw...

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  5. Show that a median of a triangle divides it into two triangles of eq...

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  6. A B C D is a trapezium with A B || D C. A line parallel to A C inters...

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  7. Diagonals A C and B D of a quadrilateral A B C D intersect at O in suc...

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  8. Let A B C D be a parallelogram of area 124c m^2dot If E and F are the ...

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  9. If A B C D is a parallelogram, the prove that a r( A B D)=a r( B C D...

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  10. Triangles on the same base and between the same parallels are equal ...

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  11. Triangles having equal areas and having one side of one of the trian...

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  12. In Figure, A B C D is a parallelogram and E F C D is a rectangle. Al...

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  13. If E ,F ,G and H are respectively the mid-points of the sides of a ...

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  14. In Figure, P is a point in the interior of a parallelogram A B C D . S...

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  15. In Figure, P Q R S and A B R S are parallelograms and X is any point o...

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  16. The diagonals of a parallelogram A B C D intersect at a point Odot Thr...

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  17. E , F , G , H are respectively, the mid-points of the sides of parall...

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  18. The side A B of a parallelogram A B C D is produced to any point Pdot ...

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  19. In Figure, B C ||X Y ,B X||C A and A B|| YC Prove that: a r( A B X...

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  20. The medians B E and C F of a triangle A B C intersect at G . Prove tha...

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