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)

Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals. Given: A rhombus A B C D such that its diagonals A C\ a n d\ B D intersect at O . To Prove: a r\ (r hom b u s\ A B C D)=1/2 (area of the rectangle contained by its diagonals =1/2(A C\ times\ B D)

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)

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)

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)

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 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 .

The diagonals of a rectangle A B C D intersect in Odot If /_B O C=68^0, find /_O D Adot

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.

The area of a trapezium is half the product of its height and the sum of parallel sides. GIVEN : A trapezium A B C D in which A B || C D ; A B=a ,D C=b and A L=C M=h , where A L_|_D C and C M_|_A B . TO PROVE : a r(t r a p. A B C D)=1/2h(a+b) construction : Join A C