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)

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\ (para l l e l o g r a m A B C D)

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 B C D is a parallelogram. Prove that: a r( B C P)=a r( D P Q) CONSTRUCTION : Join A Cdot

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)

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)

A B C D is a parallelogram X and Y are the mid-points of B C and C D respectively. Prove that a r( A X Y)=3/8a r(^(gm)A B C D) GIVEN : A parallelogram A B C D in which X and Y are the mid-points of B C and C D respectively. TO PROVE : a r( A X Y)=3/8a r(^(gm)a b c d) CONSTRUCTION : Join B Ddot

A B C D is a parallelogram X and Y are the mid-points of B C and C D respectively. Prove that a r( A X Y)=3/8a r(^(gm)A B C D)

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 A B C , A D and B E are altitudes. Prove that (a r( D E C))/(a r( A B C))=(D C^2)/(A C^2)

The mid points of the sides of a triangle A B C along with any of the vertices as the fourth point make a parallelogram of area equal to: a r\ ( A B C) (b) 1/2a r\ ( A B C) 1/3a r\ ( A B C) (d) 1/4\ a r\ ( A B C)