In Fig.9.29, `a r\ (B D P)\ =\ a r\ (A R C)`and `a r\ (B D P)\ =\ a r\ (A R C)`. Show that both the quadrilaterals ABCD and DCPR are trapeziums.

In Figure, A P || B Q\ || C R . Prove that a r\ ( A Q C)=\ a r\ (P B R)

If each diagonal of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D are such that a r( A B D)=a r( C D B ) and a r( A B C)=a r( A C D)dot TO PROVE: Quadrilateral A B C D is a parallelogram.

Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect at O in such a way that a r\ ( A O D)=a r\ (\ B O C)dot Prove that A B C D is a trapezium.

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that a r(A O D)= a r(B O C)dot Prove that ABCD is a trapezium.

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 Fig.82, line C A_|_A B and A B || C R and P R || B D. Find /_x ,/_y\ a n d\ /_zdot

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 a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

Diagonals A C and B D of a quadrilateral A B C D intersect at O in such a way that a r( A O D)=a r( B O C) . Prove that A B C D is a trapezium.

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , b a n d c are in AdotPdot