BPT applies to a line that is parallel to one side of a triangle and cuts the other two sides. In triangle ABC, to which of these lines does BPT NOT apply?

BPT needs the parallel line to cross the other two sides at genuine interior points, producing two segments on each. A line through A parallel to BC touches AB and AC only at the shared endpoint A, so it cuts off no segments and there is nothing to be proportional. The other three lines each cross two sides properly — note that BPT is not tied to the letters A, B, C or to the "base"; any side may play the role of the third side.