Show that the diagonals of a parallelogram divide it into four triangles of equal area. GIVEN : A parallelogram `A B C D` . The diagonals `A C` and `B D` intersect at `Odot` TO PROVE : `a r( O A B)=a r( O B C)=a r( O C D)=a r( A O D)`

Show that the area of a rhombus is half the product of the lengths of its diagonals. GIVEN : A rhombus A B C D whose diagonals A C and B D intersect at Odot TO PROVE : a r(r hom b u sA B C D)=1/2(A C*B D)

Show that the area of a rhombus is half the product of the lengths of its diagonals. GIVEN : A rhombus A B C D whose diagonals A C and B D intersect at Odot TO PROVE : a r(r hom b u sA B C D)=1/2(A CxB D)

In a parallelogram A B C D diagonals A C and B D intersect at O and A C=6. 8c m and B D=13. 6c m . Find the measures of O C and O D .

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.

The diagonals of quadrilateral A B C D ,A C and B D intersect in Odot Prove that if B O=O D , the triangles A B C and A D C are equal in area. GIVEN : A quadrilateral A B C D in which its diagonals A C and B D intersect at O such that B O = O Ddot TO PROVE : a r( A B C)=a r( A D C)

In a parallelogram A B C D , the bisectors of /_A\ a n d\ /_B meet at Odot Find /_A O Bdot

The diagonals of quadrilateral A B C D intersect at O . Prove that (a r( A C B))/(a r( A C D))=(B O)/(D O)

A B C D is a parallelogram whose diagonals A C and B D intersect at Odot A Line through O intersects A B at P and D C at Qdot Prove that a r( P O A)=a r( Q O C)dot

In a parallelogram A B C D diagonals A C\ a n d\ B D intersect at O\ a n d\ A C=6. 8\ c m\ a n d\ B D=5. 6 c m . Find the measures of O C\ a n d\ O D .

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.