Playing with Constructions | Class 6 Mathematics Notes

Constructing a Perpendicular Bisector of a Line Segment

A perpendicular bisector of a line segment is a line that divides the segment into two equal parts at a 90° angle. To construct it for a line segment AB, follow these steps: Place the compass pointer at point A and draw arcs above and below the line segment with a radius more than half of AB. Without changing the compass width, repeat the same from point B, creating two intersection points of the arcs above and below the segment. Join these intersection points with a straight line using a ruler. This line is the perpendicular bisector of AB, dividing it into two equal parts at a right angle. The point where this bisector crosses AB is the midpoint of the segment. This construction is fundamental in geometry and is used in constructing triangles, squares, and other polygons.

📊 Diagram: You will have to open up the compass against a ruler (see Fig. 8.2)

🧪 Activity: Construct perpendicular bisectors of various line segments and verify the midpoint by measuring lengths.

🔗 Connection: Prepares for constructing angles, starting with a 60° angle.