SOLUTION: 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? I. Three

Question 337609: 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?
I. Three
II. Four
III. Five
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
D
Draw two parallel lines. Then draw the other two lines such that those two lines intersect on one of the parallel lines. IN that case, ther eare three points where lines intersect.
Do that same two parallel lines. Now draw the other two lines such that they intersect at a point NOT on either of the two parallel lines. In that case, there will be 5 points where the lines intersect.
The only way to get 4 points, is if the other two lines are parallel to each other and NOT parallel to the first set of two lines.

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