Given: l and m are parallel. p and q are ⊥ to l and m.
To prove: p and q are parallel to each other.
Proof:
Parallel lines l and m are cut by a transversal p, ∠ 1 = ∠ 3 (Corresponding angles)
Given that p is ⊥ to l and m.
⇒ ∠ 1 = ∠ 3 = 90° ……………………….(i)
Similarly parallel lines l and m are cut by a transversal q, ∠ 2 = ∠ 4(Corresponding angles)
Given that q is ⊥ to l and m.
⇒ ∠ 2 = ∠ 4 = 90° ………………………..(ii)
From (i) and (ii), ∠ 1= ∠ 2 = 90° and ∠ 3 = ∠ 4 = 90°
One pair of corresponding angles are equal, then the two lines are parallel.
∴ p and q are parallel to each other.