Constructions | Class 7 Mathematics Notes

Constructing a Perpendicular Bisector of a Line Segment

This section explains the step-by-step process of constructing the perpendicular bisector of a given line segment AB. The perpendicular bisector is a line that divides the segment into two equal parts at a 90° angle. The construction uses a compass and straightedge without measuring the length or angles. The process begins by placing the compass pointer at point A and drawing arcs above and below the line segment with a radius more than half the length of AB. Without changing the compass width, the same arcs are drawn from point B, intersecting the previous arcs at two points. A straight line is then drawn through these two intersection points using the straightedge. This line is the perpendicular bisector of AB. The section explains why this construction works: the intersection points are equidistant from A and B, so the line joining them is perpendicular and bisects AB. This construction is fundamental in geometry and is used in many other constructions and proofs. The section also highlights the properties of the perpendicular bisector, such as any point on it being equidistant from the endpoints of the segment.

📊 Diagram: The diagrams show a line segment AB with arcs drawn from points A and B intersecting above and below the segment. The perpendicular bisector is drawn through the intersection points, clearly showing the right angle and equal segments.

🧪 Activity: Activity: Construct the perpendicular bisector of a given line segment using a compass and ruler, then verify that the two parts are equal using a ruler.

🔗 Connection: This section prepares students for constructing perpendicular lines from a point on or outside a line, which is covered in the next section.