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The diagonals AC and BD of a quadrilateral ABCD intersects each other at O such that `DeltaAOD=DeltaBOC`. Prove that ABCD is trapezium.

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The diagonals of a quadrilateral ABCD intersect each other at point ‘O’ such that (AO)/(BO) = (CO)/(DO) . Prove that ABCD is a trapezium

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In the trapezium ABCD, AB || DC. The diagonals AC and BD of it intersects each other at O. Prove that DeltaAOD=DeltaBOC.

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ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(DeltaAOD) = ar(DeltaBOC) . (Hint: Congruent figures have equal area)

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CALCUTTA BOOK HOUSE-THEOREMS ON AREAS-EXERCISE-3
  1. In the isosceles DeltaABC, AB = AC , O is any point on the side BC. OP...

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  2. In the trapezium ABCD, AB || DC. The diagonals AC and BD of it interse...

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  3. Prove that the line segment joining the mid-points of the lateral side...

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  4. Side of a equilateral triangle is 7 ,find its hight.

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  5. If a square and a rhombus lie on the same base, then find logically wh...

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  6. Prove that the area of a rhombus is half the area of the rectangle pro...

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

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  8. If E be the mid-point of the median AD of DeltaABC, then prove that De...

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  9. Prove that two diagonals of a parallelogram divides it into four trian...

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  10. P is any point on AD, the median of DeltaABC. Prove that DeltaABP=Delt...

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  11. P is any point in the interior of the parallelogram ABCD. Prove that D...

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  12. In the trapezium ABCD, AB || DC and the diagonals AC and BD intersects...

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  13. The diagonals AC and BD of a quadrilateral ABCD intersects each other ...

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  14. D and E lie on the side AB and AC of DeltaABC such that DeltaDBC=Delta...

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  15. Prove that if each diagonal of a quadrilateral bisects it into two tri...

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  16. Find the co ordinate on the X axis cut by the straight line 2x+3y=12

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  17. On the outside of the equilateral triangle ABC and in the angular regi...

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  18. D is the mid-point of the side BC of the DeltaABC and P is any point o...

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  19. Prove that the sum of the perpendiculars drawn from any interior point...

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  20. B is a vertex of the isosceles triangle ABC. D and E are the mid-point...

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