Question

L, M and N are three lines in the same plane, such that L intersects M and M||N. Show that L intersects N also.

Answer 1

To prove: L intersects N.
Proof : Suppose L does not intersect N.
This means that lines L and N are coplanar.
Therefore, L should be parallel to N.
$$\begin{gathered} \text{But M∥N (given)} \\ \text{And N∥M} \end{gathered}$$
But this is a contradiction of the hypothesis.
Thus, our supposition is wrong and L intersects N.
Hence proved.