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.

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 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 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.

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

The diagonals of a quadrilateral ABCD intersect each other at the point O such that (A O)/(B O)=(C O)/(D O) . Show that ABCD is a trapezium.

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\ a n d\ B D of a trapezium A B C D with A B||D C intersect each other at O . Prove that a r\ ( A O D)=\ a r\ ( B O C) .

Suppose line segments A B and C D intersect at O in such a way that A O=O D and O B=O C . Prove that A C=B D but A C may not be parallel to B D .

In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that O B" "=" "O D . If A B" "=" "C D , then show that: (i) a r" "(D O C)" "=" "a r" "(A O B) (ii) a r" "(D C B)" "=" "a r" "(A C B) (iii) D A" "||" "C

In Figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that O B = O D . If A B = C D , then show that: (i) a r /_\(D O C) = a r /_\(A O B) (ii) a r /_\(D C B) = a r /_\(A C B) (iii) D A || CB