Question

a point o inside a rectangle abcd is joined to the vertices.prove that the sum of the areas of a pair of opposite triangle so formed is equal to the sum of the areas of the other pair of triangles

Answer 1

To prove: Area (∆AOD) + Area (∆BOC) = Area (∆AOB) + Area (∆COD)

Draw EOF ║ AB and LOM ║ AD
To prove: Area (∆AOD) + Area (∆BOC) = Area (∆AOB) + Area (∆COD)

Draw EOF ║ AB and LOM ║ AD
Now

From (i) and (ii),

Area (∆AOD) + Area (∆BOC) = Area (∆AOB) + Area (∆COD)