Drawing a circle: One of the most basic and common uses of a compass is to draw a perfect circle. By placing the point of the compass on a specific point and rotating the pencil end around it, a circle of any desired radius can be drawn.

Constructing perpendicular lines: To construct a perpendicular line to a given line at a specific point, a compass can be used. By drawing two arcs of equal radius from the point on the line, the intersections of these arcs will determine the perpendicular line.

Bisecting an angle: To bisect an angle, a compass can be used to draw arcs from the two sides of the angle. The point where these arcs intersect will be the bisector of the angle.

Constructing parallel lines: To construct a parallel line to a given line through a specific point, a compass can be used. By drawing an arc from the point on the line and then drawing another arc from a point on the line above or below it, the intersections of these arcs will determine the parallel line.

Constructing regular polygons: A compass can be used to construct regular polygons with a specific number of sides. By using the compass to divide the circumference of a circle into equal parts, the vertices of the polygon can be determined.

Constructing tangents: A compass can be used to construct a tangent line to a circle from a specific point outside the circle. By drawing an arc from the point that intersects the circle at two points, the line connecting these two points will be the tangent line.

Constructing a square: A compass can be used to construct a square by drawing four congruent circles with their centers forming a square. The intersections of these circles will determine the vertices of the square.

Constructing an equilateral triangle: A compass can be used to construct an equilateral triangle by drawing three congruent circles with their centers forming an equilateral triangle. The intersections of these circles will determine the vertices of the triangle.

Constructing a regular hexagon: A compass can be used to construct a regular hexagon by drawing six congruent circles with their centers forming a regular hexagon. The intersections of these circles will determine the vertices of the hexagon.

Constructing a golden rectangle: A compass can be used to construct a golden rectangle, which is a rectangle with a length-to-width ratio equal to the golden ratio. By using the compass to divide a line segment into two parts in the golden ratio, a rectangle with these dimensions can be constructed.