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)`

A diagonal of a parallelogram divides it into two triangles of equal area. GIVEN : A parallelogram A B C D in which B D is one of the diagonals. TO PROVE : ar ( A B D)=a r( C D B)

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.

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)

Show that a median of a triangle divides it into two triangles of equal area. GIVEN : A A B C in which A D is the median. TO PROVE : a r( A B D)=a r( A D C) CONSTRUCTION : Draw A L_|_B C

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)

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 E 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)