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

Line segments AB and CD intersect at O such that A C||D B . If /_C A B=35^0 and /_C D B=55^0 find the /_B O Ddot

In Figure, it is given that A B=B C a n d A D=E Cdot Prove that a b e ~= C B D (ii) B D=B E

Line segments A B a n d C D intersect at O such that A C D Bdot If /_C A B=45^0a n d /_C D B=55^0, then /_B O D= 100^0 (b) 80^0 (c) 90^0 (d) 135^0

The diagonals of a parallelogram A B C D intersect at OdotA line through O intersects A B\ at X\ a n d\ D C at Ydot Prove that O X=O Y

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

In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C