Question

name: munisa
line bisectors
construct a perpendicular bisector for each of the lines below. leave all
construction marks on to show your working.

Explanation:

Step1: Take a compass

Set the compass width to more than half the length of the line segment (e.g., segment \( PQ \)).

Step2: Draw arcs from one end

With the compass point on \( P \), draw arcs above and below the line segment.

Step3: Draw arcs from the other end

Without changing the compass width, place the compass point on \( Q \) and draw arcs above and below the line segment, intersecting the previous arcs at two points (let's call them \( A \) and \( B \)).

Step4: Draw the perpendicular bisector

Use a straightedge to draw a line through points \( A \) and \( B \). This line is the perpendicular bisector of \( PQ \), as it bisects \( PQ \) (since the compass was set to more than half the length, the intersection points ensure the midpoint is on \( AB \)) and is perpendicular (by the construction of arcs from both ends, the line \( AB \) is perpendicular to \( PQ \)).

Repeat these steps for each of the other line segments in the problem.

Answer:

To construct the perpendicular bisector of a line segment (e.g., \( PQ \)):

1. Set a compass to a width \( > \frac{1}{2} \) the segment’s length.
2. Draw arcs above and below the segment from \( P \).
3. Draw arcs above and below the segment from \( Q \) (same compass width), intersecting the first arcs at two points.
4. Draw a line through these two intersection points (this is the perpendicular bisector).

Repeat for all given line segments, leaving construction marks (arcs, intersection points) visible.