Triangles ABC and ABD share side AB.

Triangle ABC has area Q and triangle ABD has area R. If AD is longer than AC and BD is longer than BC, which of the following could be true?

I R> Q

II R=Q

III R < Q

I chose “I” only but the answer was E (all of them could be.) How can the second and third condition be true?

Thanks in advance!

Above is an example of *R* < *Q*. If you imagine dragging *D *downward, eventually the area of triangle *ABD* will equal the area of triangle *ABC*, and then after that it will be bigger.