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Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other.
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 pare perpendicular to m and l, respectively.
But from Eq. (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.