Question

Prove that, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also.

Answer 1

Suppose m and n are two parallel lines and line l is their transversal. Suppose line l ⊥ line m.

Let us mark the points A and B on line m, C and D on line n and P and Q on line l.

Suppose the line l intersects line m and line n at K and L respectively. 

Since, line l ⊥ line m, then ∠PKB = 90^∘.

Since, line AB || line CD and transversal PQ intersects them at K and L respectively, then

∠KLD = ∠PKB    ...(Corresponding angles)

⇒ ∠KLD = 90^∘

∴ line l ⊥ line n.