Geometric Constructions

Why Constructions?

Geometric constructions use only a compass and straight edge (ruler used as a straightedge, not for measuring) to create precise geometric figures.

Constructing a Perpendicular Bisector

1. Draw line segment AB
2. Open compass to more than half AB. Draw arcs from A above and below the line
3. Without changing compass width, draw arcs from B (they should cross the first arcs)
4. Connect the two intersection points

The resulting line bisects AB at 90° — every point on it is equidistant from A and B.

Constructing an Angle Bisector

1. Place compass at vertex V, draw an arc crossing both arms at P and Q
2. Place compass at P, draw an arc inside the angle
3. Place compass at Q (same width), draw an arc crossing the first → intersection point R
4. Draw VR — this bisects the angle exactly

Constructing a 60° Angle

Draw a line. From point A, draw an arc. From where the arc meets the line, draw another arc of the same radius. Connect A to the intersection — this forms an equilateral triangle and gives 60°.

Constructing Triangles

Given SSS (all three sides), use compass widths to mark off each side length, creating exact intersection points for the vertices.

The Locus

A locus is a set of points satisfying a condition:

• Equidistant from two points → perpendicular bisector
• Equidistant from two lines → angle bisector
• Fixed distance from a point → circle