Question

explain how to construct a line segment that is half the length of segment ab.

Explanation:

Step1: Open compass wider

Open the compass wider than half - the length of segment \(AB\).

Step2: Draw arcs from A

Place the compass at point \(A\) and draw arcs above and below the line segment \(AB\).

Step3: Draw arcs from B

Without changing the compass width, place the compass at point \(B\) and draw arcs above and below the line segment \(AB\) intersecting the previous arcs.

Step4: Draw perpendicular bisector

Use a straight - edge to draw a line connecting the intersection points of the arcs. This line is the perpendicular bisector of segment \(AB\), and the point where it intersects \(AB\) is the mid - point \(M\) of \(AB\).

Step5: Form new segment

The line segments \(AM\) and \(MB\) are each half the length of segment \(AB\). You can choose either \(AM\) or \(MB\) as the required line segment.

Answer:

Construct the perpendicular bisector of segment \(AB\) to find its mid - point \(M\). The segments \(AM\) or \(MB\) are half the length of \(AB\).