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 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)

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)

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)

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 .

A B C D is a cyclic quadrilateral whose diagonals A Ca n dB D intersect at P . If A B=D C , Prove that : P A B~= P D C P A=P Da n dP C=P B A D ll B C

A point O inside a rectangle A B C D is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the other pair of triangles. Given: A rectangle A B C D\ a n d\ O is a point inside it. O A ,\ O B ,\ O C\ a n d\ O D have been joined. To Prove: a r\ (A O D)+\ a r\ ( B O C)=\ a r\ ( A O B)+\ a r( C O D)

The diagonals of a parallelogram A B C D intersect at O. A line through O intersects A B\ at X\ a n d\ D C at Y . Prove that O X=O Y .

The area of a rhombus is 144\ c m^2 and one of its diagonal is double the other. The length of the longer diagonal is (a)12 cm (b) 16 cm (c)18 cm (d) 24 cm

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 .