Given four distinct lines, exactly two of which are parallel, which of

Black means parallel.

I don't follow the two answers posted. I agree, however, that the answer is E.

EDIT: THIS POST IS INCORRECT. UPDATED BELOW.

UPDATE: THE ABOVE ANSWER, ALSO IN PRECEDING POST, IS NOT CORRECT. APPARENTLY I CAN'T COUNT MY OWN INTERSECTION POINTS. THE CORRECT ANSWER IS IN THIS POST. If you saw the original figure, you should still be able to see it in spoiler.

THE ANSWER IS D, I and III only.

1. If you have two parallel lines, they never intersect.

2. If you have two non-parallel lines, those two intersect each other eventually at exactly one point. +1 point of intersection

3. One of the non-parallel lines will intersect the two parallel lines in two places. +2 points of intersection

4. The other non-parallel line will also intersect the two parallel lines in two places. +2 points of intersection

TOTAL POSSIBLE is 1 + 2 + 2 = 5. That's Case 1 in NEW figure. (It doesn't matter which pair of non-parallel lines you move. I just chose two with labels A and D to make it easy to see.)

But you can use #2 and #3 so that the one point where the two non-parallel lines intersect is on one of the parallel lines

Where the one intersection point between the two non-parallel lines overlaps one of the parallel lines, you have decreased the number of intersection points to three. That's Case 2.

There is no way to make four intersection points with this set of lines. (You can get two points, obviously, by using two parallel and one non-parallel line.)

I dreamed about the original post's inaccuracy. I think I should be worried.

ANSWER D: I and III only

5 points - 2 parallel and 2 intersecting with point of intersection being above the parallel lines.
will wait for OA with OE

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