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In the adjoining figure, MNPQ and ABPQ a...

In the adjoining figure, MNPQ and ABPQ are parallelogram and T is any point on the side BP. Prove that
(i) `ar(MNPQ)=ar(ABPQ)`
(ii)` ar(triangleATQ)=(1)/(2)ar(MNPQ)`.

Text Solution

Verified by Experts

`ar(MNPQ)= ar(ABPQ)` ( they have same base and lie between same parallels).
`ar(triangleATQ)=(1)/(2)ar(ABPQ)` (they have same base and lie between same parallels).
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RS AGGARWAL-AREAS OF PARALLELOGRAMS AND TRIANGLES -Exercise 11
  1. In the adjoining figure, ABCD is a quadrilateral in which diag. BD = 1...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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