Question

Prove that, If l, m, n are lines in the same plane such that l intersects m and n $\parallel$ m, then l intersects n also.

Answer 1

Given: Three lines l,m, n in the same planes such that l intersects m and n $\parallel$ m.

To prove: lines l and n are intersecting lines
Proof: Let l and n be non-intersecting lines. Then l II n
But n $\parallel$ m

So, l $\parallel$ n and n $\parallel$ m, which means l and m are non-intersecting lines.
This is a contradiction to the hypothesis that l and m are intersecting lines.
So, our supposition is wrong.
Hence, line l intersects line n.