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

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 .

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A\ a n d\ C . Prove that A B=A D\ a n d\ C B=C D

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)

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.

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect each at P . Show that: a r(/_\A P B)\ x \ a r\ (/_\ C P D) = \ a r\ (\ /_\A P D)\ \ x a r\ (\ /_\P B C)

Diagonals A C\ a n d\ 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)dot Prove that A B C D is a trapezium.

Diagonals of a quadrilateral A B C D bisect each other. If /_A=45^0, then /_B= (a) 115^0 (b) 120^0 (c) 125^0 (d) 135^0

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.