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, P is a point in the interior of a parallelogram A B C D . 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)

If A B C D is a parallelogram, the prove that a r( A B D)=a r( B C D)=a r( A B C)=a r( A C D) =1/2a r (||^(gm) A B C D)

A B C D is a parallelogram and O is any point in its interior. Prove that: (i) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(A B C D) (ii) a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D)

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

Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect each at P . Show that: a r(/_\A P B)\ x \ a r\ (/_\ C P D) = \ a r\ (\ /_\A P D)\ \ x a r\ (\ /_\P B C)

In Figure, A B C D\ a n d\ A E F D are two parallelograms? Prove that: a r\ (\ A P E):\ a r\ (\ P F A)=\ a r\ \ (Q F D)\ : a r\ (\ P F D)

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 P || B Q\ || C R . Prove that a r\ ( A Q C)=\ a r\ (P B R)

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

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)