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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 L_|_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. A B C D is a parallelogram and O is any point in its interior. Prove t...

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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. Parallelogram A B C D and rectangle A B E F have the same base A B and...

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  5. O is any point on the diagonal B D of the parallelogram A B C D. Prove...

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  6. Triangles A B C and DBC are on the same base B C with A, D on opposite...

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  7. D and E are points on sides AB and AC respectively of DeltaA B Csuch...

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  8. If the medians of a triangle A B C intersect at G , show that a r( tr...

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  9. D, E and F are respectively the mid-points of the sides BC, CA and AB...

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  10. B D is one of the diagonals of a quadrilateral A B C D. A M and C N ...

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  11. A B C D is a quadrilateral. A line through D , parallel to A C , mee...

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  12. If the median of a △ABC intersect at G. show that ar (△AGC) = ar (△AGB...

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  13. X Y is a line parallel to side B C of triangle A B C . If B E II AC a...

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  14. E , F , G , H are respectively, the mid-points of the sides A B ,B C ...

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  15. X Y is a line parallel to side B C of /\ A B C. B E || AC and C F || A...

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  16. E , F , G , H are respectively, the mid-points of the sides A B ,B C ,...

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

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  18. Any point D is taken in the base B C of a triangle A B C\ a n d\ A...

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  19. In A B C ,D is the mid-point of A B ,P is any point of B CdotC Q P D...

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  20. In a parallelogram A B C D ,E ,F are any two points on the sides A B a...

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