In the context of solving right triangles, what is the first step in the standard construction of the perpendicular bisector of segment $mn$?

• A. Place the compass at the midpoint of $mn$ and draw a circle passing through $m$ and $n$.
• B. Mark the midpoint of $mn$ by measuring its length and dividing by two.
• C. Place the compass at point $m$ and draw an arc above and below the segment that is more than half the length of $mn$.
• D. Draw a line through points $m$ and $n$.

Answer: (C)

Verified step by step guidance

1. Identify the segment \( \overline{mn} \) for which you want to construct the perpendicular bisector.
2. Place the compass point at one endpoint of the segment, for example at point \( m \).
3. Adjust the compass width to a length greater than half of the segment \( \overline{mn} \). This ensures the arcs will intersect above and below the segment.
4. Draw an arc above and below the segment \( \overline{mn} \) while keeping the compass point at \( m \).
5. Repeat the same process by placing the compass point at the other endpoint \( n \) and draw arcs that intersect the previous arcs, creating two intersection points.