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The base BC of Delta ABC is divided at D...

The base BC of `Delta ABC` is divided at D, so that `BD=1/2DC`. Prove that `ar(Delta ABD)`=`1/3ar(Delta ABC)`

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Let E be the midpoint of DC. Then,
`BD = DE = EC = (1)/(3)BC`.
Join AD and AE.
In `triangleABE,` AD is a median and so `ar(triangleABD)=ar(triangleADE)`.
In `triangleADC,` AE is a median and so `ar(triangleADE)=ar(triangleAEC)`.
`therefore ar(triangleABD)=ar(triangleADE)=ar(triangleAEC)=(1)/(2)ar(triangleABC)`.
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RS AGGARWAL-AREAS OF PARALLELOGRAMS AND TRIANGLES -Exercise 11
  1. O is the any point on diagonal PR of parallelogram PQRS. Prove that Ar...

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

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

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

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

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

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

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

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

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

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

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

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  13. In the adjoining figure, BD||CA, E is the midpoint of CA and BD =(1)/(...

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  14. The given figure shows a pentagon ABCDE.EG drawn parallel to DA meets ...

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  15. In figure, CD || AE and CY || BA. Prove that ar (DeltaCBX) = ar (Delta...

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  16. In the adjoining figure, the point D divides the sides of triangleABC ...

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  17. In a trapezium ABCD, AB || DC, AB = a cm, and DC = b cm. If M and N ar...

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  18. ABCD is a trapezium in which AB || DC, AB = 16 cm and DC = 24 cm. If E...

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  19. In figure X and Y are the mid-points of AC and AB respectively, QP || ...

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  20. In figure, ABCD and AEFD are two parallelograms. Prove that ar (DeltaP...

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