Question

Question 5
Prove that two lines that are respectively perpendicular to two intersecting line intersect each other.

Answer 1

Let lines l and m are two intersecting lines. Again, Let n and p be another two lines which are perpendicular to the intersecting lines meet at point D.

To prove: Two lines n and p intersect at the point D.
Proof:
Suppose, lines n and p are not intersecting, then it means they are parallel to each other i.e., n || p ....(i)
Since, lines n and p are perpendicular to m and l, respectively.
But from Eqn. (i) n || p, it implies that l || m.
Hence, it is a contradiction.
Thus, our assumption is wrong.
Therefore, lines n and p interset at a point.