Question
Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.
✓
Answer
Let the two parallel lines be m and n. Let p ⊥ m.$\Rightarrow\angle1=90^\circ$Let q ⊥ n.$\Rightarrow\angle2=90^\circ$
Now, m || n and p is a transversal.$\Rightarrow\angle1=\angle3$ (corresponding angles)
$\Rightarrow\angle3=90^\circ$
$\Rightarrow\angle3=\angle2$ (each 90°)
But, these are corresponding angles, when transversal n cuts lines p and q.$\therefore$ p || q.
Hence, two lines which are perpendicular to two parallel lines, are parallel to each other.
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