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A diagonal of a parallelogram divides it...

A diagonal of a parallelogram divides it into two triangles of equal area. GIVEN : A parallelogram `A B C D` in which `B D` is one of the diagonals. TO PROVE : ar `( A B D)=a r( C D B)`

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`In /_\ABD and /_\CBD`
`AD=BC->"(opposite sides of parallelogram)"`
`AB=CD->"(opposite sides of parallelogram)"`
`BD=BD->(common)`
`"SSS congruency rule "`
`/_\ABDcong/_\CBD`
`ar(/_\ABD)=ar(/_\CBD)`
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RD SHARMA-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. The area of a parallelogram is the product of its base and the corre...

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  2. Prove that Parallelograms on the same base and between the same parall...

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

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  4. Prove that If each diagonal of a quadrilateral separates it into two...

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  5. The area of a triangle is half the product of any of its sides and t...

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  6. Triangles A B C and +DBC are on the same base B C with A, D on opposit...

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

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

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

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  10. 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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  11. 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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  12. Show that the diagonals of a parallelogram divide it into four trian...

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

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

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

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

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

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