Question

question 1 - 3
line segment ( overline{mn} ) is shown below
what is the best step in the student construction of the perpendicular bisector of ( overline{mn} )?

• use a straightedge to draw a line perpendicular to line segment ( overline{mn} )
• use a straightedge to draw a line parallel to line ( overline{mn} )
• use a compass to draw one arc with point ( m ) at the center and intersecting point ( n )
• use a compass to draw two intersecting arcs with centers at points ( m ) and ( n )

Explanation:

Step1: Analyze each option

• Option 1: Using a straightedge to draw a line perpendicular to \( \overline{MN} \) without knowing the mid - point is not the first step of constructing the perpendicular bisector.
• Option 2: Using a straightedge to draw a line parallel to \( \overline{MN} \) is not relevant to constructing the perpendicular bisector.
• Option 3: Using a compass to draw one arc with center \( M \) and intersecting \( N \) is not sufficient for constructing the perpendicular bisector.
• Option 4: When constructing the perpendicular bisector of a line segment \( \overline{MN} \), the first step is to use a compass to draw two intersecting arcs with centers at \( M \) and \( N \) (with the same radius greater than \( \frac{1}{2}MN \)). Then, we can connect the intersection points of these arcs to get the perpendicular bisector.

Answer:

Use a compass to draw two intersecting arcs with centers at points \( M \) and \( N \)