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.