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

The diagonals of quadrilateral `A B C D ,A C` and `B D` intersect in `Odot` Prove that if `B O=O D ,` the triangles `A B C` and `A D C` are equal in area. GIVEN : A quadrilateral `A B C D` in which its diagonals `A C` and `B D` intersect at `O` such that `B O` = `O Ddot` TO PROVE : `a r( A B C)=a r( A D C)`

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Verified by Experts

`In/_ABD`
`OB=OD`
O is the midpoint of BD
AD is the median
`ar(/_AOB)=ar(/_AOD)-(1)`
`In/_CBD`
`OB=OD`
O is the midpoint, OC is the median
...
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RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O ...

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  2. If P is any point in the interior of a parallelogram A B C D , then pr...

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  3. The diagonals of quadrilateral A B C D ,A C and B D intersect in Odot ...

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  4. X Y is a line parallel to side B C of triangle A B C. BE ll AC and C...

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  5. In Figure, A B C D is a trapezium in which A B D C and D C=40c m and ...

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  6. Show that the diagonals of a parallelogram divide it into four tria...

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  7. Show that the area of a rhombus is half the product of the lengths o...

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  8. A B C D is a parallelogram whose diagonals A C and B D intersect at Od...

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  9. A point D is taken on the side B C of a A B C such that B D=2d Cdot P...

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  10. In Figure, D , E are points on sides A B and A C respectively of A B ...

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  11. A B C is a triangle in which D is the mid-point of B C and E is the mi...

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  12. In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D ...

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  13. A B C D is a parallelogram X and Y are the mid-points of B C and C D r...

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  14. The area of a trapezium is half the product of its height and the su...

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

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

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  17. Prove that the area of a rhombus is equal to half the rectangle cont...

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

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

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

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