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If `P` is any point in the interior of a parallelogram `A B C D` , then prove that area of the triangle `A P B` is less than half the are of parallelogram.

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`ar(/_\APB)=1/2xxABxxPM`
`PM"<"DN`
`ABxxPM"<"ABxxDN`
`1/2xxABxxPM<1/2xxABxxDN`
`ar(/_\APB)"<"1/2 ar("parallelogram "ABCD)`
`ar(/_\ADB)"<"ar("parallelogram "ABCD)`
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RD SHARMA-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. Triangles A B C and +DBC are on the same base B C with A, D on opposit...

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  2. If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O ...

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  3. If P is any point in the interior of a parallelogram A B C D , then pr...

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  4. Prove that the diagonals of quadrilateral A B C D ,A C and B D interse...

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  5. X Y isa line parallel to side B C of A B CdotB E A and C F A B meet...

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  6. In Figure, A B C D is a trapezium in which A B D C and D C=40c m and ...

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  7. Show that the diagonals of a parallelogram divide it into four trian...

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  8. Show that the area of a rhombus is half the product of the lengths o...

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  9. A B C D is a parallelogram whose diagonals A C and B D intersect at Od...

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  10. A point D is taken on the side B C of a A B C such that B D=2d Cdot P...

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  11. In Figure, D , E are points on sides A B and A C respectively of A B ...

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  12. A B C is a triangle in which D is the mid-point of B C and E is the mi...

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  13. In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D ...

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  14. A B C D is a parallelogram X and Y are the mid-points of B C and C D r...

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  15. The area of a trapezium is half the product of its height and the s...

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  16. Parallelogram A B C D and rectangle A B E F have the same base A B and...

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  17. O is any point on the diagonal B D of the parallelogram A B C Ddot Pro...

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  18. Prove that the area of a rhombus is equal to half the rectangle cont...

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  19. A quadrilateral A B C D is such that diagonal B D divides its area in ...

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  20. Two Trinangle having the same base and equal areas lie between the sam...

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