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`

In Figure A B C D\ a n d\ A E F D are two parallelograms. Prove that: P E=F Q

In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prove that a r( A D E)=a r( B C F)

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, A B C D is a trapezium in which A B||C D . Prove that: a r( A O D)=a r( B O C)dot

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, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A Cdot GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r( A B D)=a r( B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A L_|_B D and C M B Ddot TO PROVE : A O=O Cdot

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)

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

In Figure, A B C D is a parallelogram and E F C D is a rectangle. Also A L _|_D Cdot Prove that a r(A B C D=a r(E F C D) a r (a A B C D)=D C x A L