Question

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

[Hint: Use proof by contradiction].

Answer 1

Given 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 intersecting at a point.

Proof: Suppose we consider 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 equation (i) n || p it implies that l || m.

Hence, it is a contradiction.

Thus, our assumption is wrong.

Therefore, lines n and p intersect at a point.