Diagonals `A C` and `B D` of a trapezium `A B C D` with `A B C D` intersect each where at `Odot` Prove that ar `( A O D)=a r( B O C)dot`

A B C D is a parallelogram whose diagonals A C and B D intersect at Odot A Line through O intersects A B at P and 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 Cdot A line parallel to A C intersects A B at X and B C at Ydot Prove that a r( A D X)=a r( A C Y)dot

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( A O D)=a r( B O C) . 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

Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect each at Pdot Show That: a r(A P B)\ x\ a r\ ( C P D)=\ a r\ (\ A P D)\ \ x\ \ a r\ (\ P B C)

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

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that a r" "(A P B)" "xx" "a r" "(C P D)" "=" "a r" "(A P D)" "xx" "a r" "(B P C)dot

In Figure, A B C D is a trapezium in which A B||D C ,\ \ D C is produced to E such that C E=A B , prove that a r( A B D)=a r\ ( B C E)dot Construction: Draw D M\ on B A produced and B N_|_D C