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)` .

Diagonals A C and B D of a trapezium A B C D with A B || C D intersect each other at O . Prove that ar ( triangle A O D)=a r( triangle B O C) .

Diagonal A C\ a n d\ B D of trapezium A B C D , in which A B || D C , intersect each other at Odot The triangle which is equal in area of A O D is A O B (b) B O C (c) D O C (d) A D C

A B C D is a parallelogram whose diagonals A C\ a n d\ B D intersect at O . A line through O intersects A B\ a t\ P\ a n d\ D C\ at Q . Prove that a r\ (\ /_\P O A)=\ a r\ (\ /_\Q O C) .

Diagonals A C and B D of a trapezium A BC D with A B, D C intersect each other at the point O . Using similarity criterion for two triangles, show that (O A)/(O C)=(O B)/(O D) .

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.

In Figure, A B C D is a trapezium in which A B||C D . Prove that: a r( A O D)=a r( B O C)dot

A B C D is a parallelogram whose A C\ a n d\ B D intersect at Odot A line through O intersects A B\ a t\ P\ a n d\ D C\ at Qdot Prove that a r\ (\ P O A)=\ a r\ (\ Q O C)dot

A B C D is a trapezium with A B||D C . A line parallel to A C intersects A B at X a n d B C at Ydot Prove that a r( A D X)=a r( A C Y)dot

ABCD is a trapezium in which AB||DC and its diagonals intersect each other at the point O. Show that (A O)/(B O)=(C O)/(D O) .