Basic constructions
Japanese school year: Junior high 1
What you learn
Learn how to construct perpendicular bisectors, angle bisectors, and perpendicular lines using only a compass and straightedge. This requires understanding the properties of circles and equidistant points. Geometric construction is widely used to locate points satisfying specific geometric conditions and to verify geometric theorems.
Key points
This method constructs a perpendicular bisector, a line passing through a segment's midpoint at a right angle. Draw arcs of equal radius from both endpoints, then connect their intersections.
This method constructs an angle bisector, which divides an angle into two equal parts. Draw equal arcs from two equidistant points on the angle's rays, and connect their intersection to the vertex.
This method constructs a perpendicular line through a given point. Mark two equidistant points on the line using an arc centered at the point, then construct their perpendicular bisector.
Choose a set to practice.