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`

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 as shown in Figure. Show that ar(||^(gm) ABCD)=ar (||^(gm) PBQR)

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)

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

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 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

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)

The diagonals of a parallelogram A B C D intersect at a point Odot Through O , a line is drawn to intersect A D\ at P and B C at Qdot Show that P Q divides the parallelogram into two parts of equal area.

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( A D F)=a r( D C E)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) a r\ (A E D F)=a r\ (A B C D E)

In Figure, P Q R S and A B R S are parallelograms and X is any point on side B Rdot Show that : a r(^(gm)P Q R S)=a r(^(gm)A B R S) a r(A X S)=1/2a r( P Q R S)