If p, m, n are three lines such that p || m and n ⊥ p, prove that n ⊥ m.

p || m (Given) and n is a transversal cutting p and m.
Let ∠a and ∠b be two angles made by p and m when cut by a transversal.
∴ ∠ a = ∠ b = 90° (Since it is given that n ⊥ p) 
Since n is intersecting m and ∠ b is 90°
∴ n ^ m.
Hence proved.