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 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.

If each diagonals of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram.

If each diagonals of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram.

In Figure, compute the area of quadrilateral A B 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(triangle A O D)=a r(triangle B O C) . Prove that A B C D is a trapezium.

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 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.