Consider the case of a rectangle ABCD, with diagonals AC and BD drawn. Now, it's easy to see that triangles ADC and BCD are congruent. So, the ratio of their areas would be 1. But when I try to obtain the same result via the common base theorem, the line passing through A and B never meets the base DC (as AB and DC are parallel!). How is this possible, when the ratio of the areas is known to be finite?! Or does this situation imply that the Common Base theorem can't be applied in such cases?