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