Find a counterexample for the conjecture
three coplanar lines always make a triangle.

Question

Find a counterexample for the conjecture
three coplanar lines always make a triangle.

ybarrap · Answer

If 3 lines are collinear, then they do not span more than a line:

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anonymous · Answer

If you have an system, $S$ of the following:
$$S=\left\{\eqalign{
&y=ax+c_1 \
&y=ax+c_2 \
&y=ax+c_3 \
}\right.$$
They will never intersect. In other words, if they had the same slope, they would never form a triangle

debbieg · Answer

Even if just two are parallel, then no triangle can be formed.

anonymous · Answer

As well If you had a system where the three lines intersected eachother ONLY ONCE. Such as in the case of:
$$S=\left\{\eqalign{
&y=m_1(x-h)+k \
&y=m_2(x-h)+k \
&y=m_3(x-h)+k \
}\right.$$
Which has the solution $(h,k)$