Question

1. here are 2 points in the plane. explain how to construct a line segment that is half the length of segment ab. (from unit 1, lesson 3.)

Explanation:

Step1: Draw arcs

Place the compass at point A. Open the compass to a radius greater than half of the length of segment AB. Draw arcs above and below the segment. Then, without changing the compass - width, place the compass at point B and draw arcs that intersect the previously drawn arcs.

Step2: Draw the perpendicular bisector

Use a straight - edge to draw a line connecting the two intersection points of the arcs. This line is the perpendicular bisector of segment AB. Let the mid - point of segment AB be M, which is the intersection of the perpendicular bisector and segment AB.

Step3: Identify the half - length segment

The line segment AM (or BM) is half the length of segment AB.

Answer:

1. First, use a compass to draw arcs from points A and B to construct the perpendicular bisector of segment AB. The intersection of the perpendicular bisector and segment AB gives the mid - point M. 2. The line segment AM (or BM) is the line segment that is half the length of segment AB.