Constructing triangles

Building a triangle with compasses from three given sides.

The perpendicular bisector

Constructing the perpendicular bisector of a segment with compasses.

A perpendicular from a point to a line

Dropping a perpendicular from an external point with compasses.

A perpendicular at a point on a line

Erecting a right angle at a marked point on a line.

The angle bisector

Cutting an angle exactly in half with compasses.

Loci at a fixed distance

The circle of points at a fixed distance from a point.

Equidistant from two points

Why the points equidistant from A and B form the perpendicular bisector of AB.

Equidistant from two lines

Why the points equidistant from two intersecting lines lie on the angle.

Combining loci into regions

Shading the region that satisfies several conditions at once.