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

Explanation

To prove that two lines \( p \) and \( q \) are parallel to each other when they are both perpendicular to two parallel lines \( m \) and \( n \), we can follow these steps:

### Step 1: Understand the Given Information
We are given two parallel lines \( m \) and \( n \). Lines \( p \) and \( q \) are perpendicular to these lines.

### Step 2: Identify the Angles
Since \( p \) is perpendicular to \( m \), the angle formed between line \( p \) and line \( m \) is \( 90^\circ \). Similarly, since \( q \) is perpendicular to \( n \), the angle formed between line \( q \) and line \( n \) is also \( 90^\circ \).

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