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Assertion (A) : In a trapezium ABCD, we ...

Assertion (A) : In a trapezium ABCD, we have AB ||DC and the diagonals AC and BD intersect at O.
Then, `ar(triangleAOD)= ar(triangleBOC)`.

Reason (R ) : Triangle on the same base between the same parallels are equal in area.

Text Solution

Verified by Experts

`ar(triangleCDA)=ar(triangleCDB)` (`triangle` on the same base and between the same parallels)
`rArr ar(triangleCDA)-ar(triangleOCD)=ar(triangleCDB)-ar(triangleOCD)`.
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RS AGGARWAL-AREAS OF PARALLELOGRAMS AND TRIANGLES -Exercise 11
  1. P and Q are any two points lying on the sides DC and AD respectively ...

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  2. In the adjoining figure, MNPQ and ABPQ are parallelogram and T is any ...

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  3. Assertion (A) : In a trapezium ABCD, we have AB ||DC and the diagonals...

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  4. In figure, if DEabs()BC, then find the ratio of ar (DeltaADE) and ar(D...

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

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  6. A diagonal of a parallelogram divides it into two triangles of equal a...

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  7. In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If l...

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  8. The points D and E are respectively located on AB and AC on the sides ...

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  9. O is the any point on diagonal PR of parallelogram PQRS. Prove that Ar...

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  10. In the adjoining figure, the diagonals AC and BD of a quadrilateral AB...

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  11. The vertex A of triangle ABC is joined to a point D on the side BC. Th...

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  12. D is the midpoint of side BC of triangleABC and E is the midpoint of ...

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  13. In trapezium ABCD, AB || DC and L is the mid-point of BC. Through L, a...

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  14. In the adjoining figure, ABCD is a quadrilateral. A line through D, p...

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  15. In the adjoining figure, triangle ABC and triangleDBC are on the same ...

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  16. ABCD is a parallelogram in which BC is produced to E such that CE = BC...

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  17. A point E is taken on the side BC of a parallelogram ABCD. AE and DC a...

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  18. P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and ...

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  19. किसी त्रिभुज ABC की मधिकाएँ CD और BE एक दूसरे को O पर कटती है , तो अन...

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  20. The base BC of Delta ABC is divided at D, so that BD=1/2DC. Prove that...

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