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In the trapezium ABCD, AB || DC. The dia...

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

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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.

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)

In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

In trapezium ABCD , BC||AD and AD=4cm . The two diagonals AC and BD intersect at the point O in such a way that (AO)/(OC)=(DO)/(OB)=(1)/(2) . Find the length of BC .

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

In a trapezium ABCD, BC AD and AD = 4 cm. the two diagonals AC and BD intersect at the point O in such a way that AO/OC = DO/OB = 1/2. Calculate the length of BC.

P is any point on the diagonal BD of the parallelogram ABCD. Prove that DeltaAPD=DeltaCPD .

In trapezium ABCD, BC||AD and AD = 4cm. Diagonals AC and BD intersect at O. If (AO)/(OC)= (DO)/(OB)=1/2 then find the length of BC.

Kamala have drawn a trapezium PQRS of which PQ||SR . If the diagonals PR and QS intersect each other at O , then prove that OP:OR=OQ:OS , If SR=2PQ , then prove that O is a point of trisection of both the diagonals.

P is any point on BC of the square ABCD. The perpendicular , drawn from B to AP intersects DC at Q . Prove that AP = BQ.

CALCUTTA BOOK HOUSE-THEOREMS ON AREAS-EXERCISE-3
  1. A square and a rhombus stand on the same base of length 10 cms. Show t...

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  2. In the isosceles DeltaABC, AB = AC , O is any point on the side BC. OP...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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