`p\ A N D\ q` are any two points lying on the sides `D C\ a n d\ A D` respectively of a parallelogram `A B C Ddot\ ` Show that `a r( A P B)=a r\ ( B Q C)dot`

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD . Show that a r\ (A P B)\ =\ a r\ (B Q C) .

If E ,\ F ,\ G\ a n d\ H are respectively the mid-points of the sides of a parallelogram A B C D ,\ Show that a r(E F G H)=1/2a r\ (A B C D)

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(triangle A D F)=a r( triangle D C E) .

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).

In Figure, P is a point in the interior of a parallelogram A B C Ddot Show that a r( A P B)+a r( P C D)=1/2a r\ (|""|^(gm)A B C D) a r\ ( A P D)+a r\ ( P B C)=a r\ ( A P B)+a r( P C D)

In Figure, A N and C P are perpendicular to the diagonal B D of a parallelogram A B C Ddot Prove that : A D N~= C B P (ii) A N=C P

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(llgm A B C D)=a r(llgm B P R Q)dot CONSTRUCTION : Join A C and PQ. TO PROVE : a r(llgm A B C D)=a r(llgm B P R Q)

In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)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)

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P || B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q) .