`A B C D` is a quadrilateral. A line through `D ,` parallel to `A C ,` meets `B C` produced in `P` as shown in Figure. Prove that `a r\ ( A B P)=a r\ (Q u a ddotA B C D)dot`

The side A B of a parallelogram A B C D is produced to any point Pdot A line through A and parallel to C P meets C B produced at Q and then parallelogram P B Q R is completed as shown in Figure. Show that a r(^(gm)A B C D)=a r ^(gm)P B Q R)dot

In Figure, A B C D E is a pentagon. A line through B parallel to A C meets D C produced at Fdot Show that a r( A C B)=a r( A C F) (ii) a r( A E D F)=a r(A B C D E)

In Figure, A B C D E\ is a pentagon. A line through B parallel to A C meets D C produced at Fdot Show that: a r\ ( A C B)=a r\ ( A C F) a r\ (A E D F)=a r\ (A B C D E)

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that a r" "(A B C D)" "=" "a r" "(P B Q R)dot

The side A B of a parallelogram A B C D is produced to any point Pdot A line through A parallel to C P meets C B produced in Q and the parallelogram P B Q R completed. Show that a r(^(gm)A B C D)=a r(^(gm)B P R Q)dot CONSTRUCTION : Join A C and PQ. TO PROVE : a r(^(gm)A B C D)=a r(^(gm)B P R Q)

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 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

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

P is the mid-point of side A B of a parallelogram A B C D . A line through B parallel to P D meets D C at Q\ a n d\ A D produced at Rdot Prove that: A R=2B C (ii) B R=2\ B Q

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