<p>Four distinct lines lie in a plane, and exactly two of them are parallel. Which of the following could be the number of points where at least two of the lines intersect?</p>
<p>Three
Four
Five</p>
<p>A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III</p>
<p>I believe the answer is E but according to collegeboard, it is actually D. However, I can create 4 point of intersection if I place the 2 non parallel lines over the parallel ones in a nonparallel fashion. Can someone help explain?</p>
<p>You have to remember that lines go on forever. That means that eventually, the two non-parallel lines you drew will intersect, again creating five intersections, not four.</p>
<p>It is D. For there to be four points of intersection, there would have to be two sets of parallel lines, and the question says exactly two lines are parallel.</p>
<p>It''s D because it says exactly two lines are parallel. The only way to get 4 intersections is if you have 2 pairs of parallel lines. Since that isn't the case, only I (both nonparallel lines intersect on one of the parallel lines) and III (both nonparallel lines intersect outside of the parallel lines) can be true</p>
<p>That picture depicts line segments, not lines. Lines go on forever, and therefore the two non-parallel lines will cross on top, forming an intersection. Imagine extending those four lines infinitely. You will find that there are five intersections. It's a postulate of Euclidean geometry.</p>
<p>That picture is misleading because it is cut off.</p>
<p>If the point of intersection of the two non-parellel lines is also on a parallel line, a triangle will be created, and there will be exactly three points of intersection.</p>
