Given below is a parallelogram `A B C Ddot\ ` Complete each statement along with the definition or property used.
(i)`A D=`
(ii) `/_D C B=`
(iii)`O C=`
(iv) `/_D A B+/_C D A=`

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)

The diagonals of a parallelogram A B C D intersect at Odot A line through O meets A B in X and C D in Ydot Show that a r( A X Y D)=1/2(A R ^(gm)A B C D)

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X A Y B\ ~= C X D (iv) A X D~=\ C Y B

If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O , and seqarate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D intersect at O and separate it into four parts such that a r( A O B)=a r( B O C)=a r( C O D)=a r( A O D) TO PROVE : Quadrilateral A B C D is a parallelogram.

In Figure, A B C D is a parallelogram in which /_D A O=40^0, /_B A O=35^0 a n d /_C O D=65^0dot Find: /_A B O (ii) /_O D C (iii) /_A C B (iv) /_C B D

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

If A B C is an isosceles triangle such that A B=A C and A D is an altitude from A on B C . Prove that (i) /_B=/_C (ii) A D bisects B C (iii) A D bisects /_A

If a +b gt c+d and b + c gt a+d, then it is definite that