Question

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

Given: line AB || line CD and line EF intersects them at P and Q respectively.

line EF ⊥ line AB

To prove: line EF ⊥ line CD

Answer 1

Proof: 

line EF ⊥ line AB[Given] 

∴ ∠APR = 90° ….(i) 

line AB || line CD and line EF is their transversal. 

∴ ∠EPB ≅ ∠PQD …..(ii) [Corresponding angles] 

∴ ∠PQD = 90° [From (i) and (ii)] 

∴ line EF ⊥ line CD