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)

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

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

Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect each at Pdot Show That: a r(A P B)\ x\ a r\ ( C P D)=\ a r\ (\ A P D)\ \ x\ \ a r\ (\ P B C)

A B C D IS A PARALLELOGRAM AND O is any point in its interior. Prove that: a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(^(gm)A B C D) Given: A parallelogram A B C D\ a n d\ O is a point in its interior. To Prove: a r\ (\ A O B)+\ a r( C O D)=a r\ ( B O C)+a r( A O D)

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)

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)

In Figure, P S D A is a parallelogram in which P Q=Q R=R S\ a n d\ A P B Q C Rdot Prove that a r\ (\ P Q E)=\ a r\ (\ C F D)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)

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