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`

O is any point on the diagonal B D of the parallelogram A B C Ddot Prove that a r( O A B)=a r( O B C)

P\ a n d\ Q are the points of trisection of the diagonal B D of a parallelogram A B C Ddot Prove that C Q is parallel to A Pdot Prove also that A C bisects P Q

In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D

In a parallelogram A B C D , write the sum of angle A\ a n d\ B

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, X ,\ Y are the mid-points of opposite sides A B\ a n d\ D C of a parallelogram A B C DdotA Y\ a n d\ D X are joined intersecting in P ; C X\ a n d\ B Y are joined intersecting in Q . Show that A X C Y is a parallelogram (ii) D X B Y\ is a parallelogram quadrilateral P X Q Y is a parallelogram

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

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)

In figure A B=A C\ a n d\ C P||B A and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A (ii) A B C P is a parallelogram

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