SOLUTION: what is the probability that three lines drawn at random can form a triangle

Question 1135997: what is the probability that three lines drawn at random can form a triangle
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.

100%.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) We are talking LINES, of infinite length -- not LINE SEGMENTS of finite length.

(2) Three lines will all intersect each other, forming a triangle, UNLESS at least two of the lines are parallel.

(3) The slope of a line can be any real number (or undefined); if the three lines are drawn at random, the probability that any two of them have EXACTLY the same slope is 0.

Therefore, there is a 100% probability that three lines drawn at random will form a triangle.
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