1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Question 10 Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.

Open in App
Solution

## Given, two lines m and n are parallel and another two lines p and q are respectively perpendicular to m and n. i.e., p⊥m, p⊥n, q⊥m, q⊥n, To prove p || q, Proof: m || n and p are perpendicular to m and n. ∴ ∠1=∠10=90∘ [corresponding angles] Similarly, ∠2=∠9=90∘ [corresponding angles] [∵ p ⊥ m and p ⊥ n] ∴ ∠4=∠10=90∘ and ∠3=∠9=90∘.........(i) [alternate interior angles] Similarly, if m || n and q is perpendicular to m and n, Then, ∠7=90∘ and ∠11=90∘.....(ii) From (i) and (ii) Now, ∠4+∠7=90∘+90∘=180∘ So, sum of two interior angles is supplementary. We know that, if a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel. Hence, p || q.

Suggest Corrections
3
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program