Can three lines intersect each other and form more than one triangle?

Expert Answers
justaguide eNotes educator| Certified Educator

Two lines can only intersect each other at a single point.

Taking pairs of two lines of the three lines we have, we see that we can select three pairs of lines. Now each of these pairs of lines intersects each other at only a single point as lines are defined as straight, with the y-coordinate of each point on the line having only one corresponding x-coordinate value and vice versa. Also, triangles are formed with only straight lines. Therefore we cannot form more than 3 triangles with the points of intersection of 3 lines.

neela | Student

3 lines can tersect  at most 3C2  = 3 points only. So 3 points of intersection  form one triangle.

If the 3 lines are parallel, then  there is no tersection of lines.Therefore , no triangle is formed.

If any ewo lines are parallel, and the 3rd is not parallel, then there one non parallel line intersect the other two parallel line at 2 points. No triangle is formed in this case.

All 3 lines can pass through one single point. We say then the  3 lines are concurrent at one point. So there one limitting point triangle of zero dimension and zero area.

So the in the first case only the 3 points of intersection  forma triangle. In no case there can be more than one triangle.