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

Given: Let n and p be two intersecting lines. Let l ⊥ n and m ⊥ p.
To Prove: l and m will intersect.
Proof:
Let n and p be two intersecting lines.
Let us assume that l and m do not intersect.
Now, l ⊥ n [Given]
l || m [By assumption]
∴ m ⊥ n …………………..(i)
Also, m ⊥ p, ……………(ii)
From (i) and (ii), we have n || p which is wrong since n and p intersect. [Given]
⇒ Our assumption is wrong.
∴ l and m intersect.