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If the diagonals `A C ,B D` of a quadrilateral `A B C D ,` intersect at `O ,` and seqarate the quadrilateral into four triangles of equal area, show that quadrilateral `A B C D` is a parallelogram. GIVEN : A quadrilateral `A B C D` such that its diagonals `A C` and `B D` intersect at `O` and separate it into four parts such that `a r( A O B)=a r( B O C)=a r( C O D)=a r( A O D)` TO PROVE : Quadrilateral `A B C D` is a parallelogram.

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If the diagonals A C ,\ B D of a quadrilateral A B C D , intersect at O , and separate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram.

If each diagonal of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D are such that a r( A B D)=a r( C D B ) and a r( A B C)=a r( A C D)dot TO PROVE: Quadrilateral A B C D is a parallelogram.

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The diagonals of quadrilateral A B C D intersect at O . Prove that (a r( A C B))/(a r( A C D))=(B O)/(D O)

If the diagonal B D of a quadrilateral A B C D bisects both /_B and /_D , show that (A B)/(B C)=(A D)/(C D) .

If the diagonal B D of a quadrilateral A B C D bisects both /_B and /_D , show that (A B)/(B C)=(A D)/(C D) .

In the figure, diagonal A C of a quadrilateral A B C D bisects the angles A and C . Prove that A B=A D and C B=CD

Diagonals A C and B D of a quadrilateral A B C D intersect at O in such a way that a r( A O D)=a r( B O C) . Prove that A B C D is a trapezium.

Show that the diagonals of a parallelogram divide it into four triangles of equal area. GIVEN : A parallelogram A B C D . The diagonals A C and B D intersect at Odot TO PROVE : a r( O A B)=a r( O B C)=a r( O C D)=a r( A O D)

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RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. The area of a triangle is half the product of any of its sides and t...

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  2. Triangles A B C and DBC are on the same base B C with A, D on opposite...

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

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

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  5. The diagonals of quadrilateral A B C D ,A C and B D intersect in Odot ...

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  6. X Y is a line parallel to side B C of triangle A B C. BE ll AC and C...

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

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

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

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

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

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

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

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  18. O is any point on the diagonal B D of the parallelogram A B C D. Prove...

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

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

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