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P and Q are any two points lying on the sides DC and AD respectively of a parallelogramABCD. Show that `a r\ (A P B)\ =\ a r\ (B Q C)`.

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`ar(triangleAPB)=(1)/(2)ar(ABCD)and ar(triangleBQC)=(1)/(2)ar(ABCD)`
[`therefore triangle` and ||gm have same base and lie between same parallels]
`therefore ar(triangleAPB)=ar(triangleBQC)`.
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RS AGGARWAL-AREAS OF PARALLELOGRAMS AND TRIANGLES -Exercise 11
  1. ABCD is a parallelogram and X is the mid-point of AB. (AXCD)= 24 cm^(2...

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  2. In the adjoining figure, ABCD is a quadrilateral in which diag. BD = 1...

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  3. P and Q are any two points lying on the sides DC and AD respectively ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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