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` and `O` is a point inside it. `O A ,O B ,O C` and `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)` CONSTRUCTION : Draw `E O F A B` and `L O M A Ddot`