Geometric Constructions

A geometric construction is a step-by-step process to determine and build a geometric figure or configuration. A configuration is a set of interrelated geometric shapes. A geometric construction is called a construction for short. Traditionally, constructions were done on paper or on a chalkboard using a writing tool, straightedge, and compass.

Nowadays, constructions can be simulated using interactive, dynamic geometry software on computers and handheld devices. Not just the software but the constructions themselves are interactive and dynamic. They are interactive because they are readily modified. They are dynamic because the user can move and manipulate the constructed geometric configuration without changing its dependency relationships.

The dependency relationships of a configuration are determined by the nature and order of the steps in the construction process. As the figure is built step by step, relationships are established by how and where the parts of the figure are attached. The configuration becomes somewhat like the skeletal system of the human body or a mechanical device with interconnected parts, levers, and linkages.

The dynamic aspect of a construction helps to reveal what changes and what stays the same when the figure is manipulated. This reveals invariants - properties of the figure determined by the inherent dependency relationships in the construction process.


Sketchpad is a dynamic visualization software package that encourages mathematical discovery. Students manipulate geometric sketches that they have constructed themselves by movements that do not change the dependency relationships. This enables them to discover invariants and make conjectures of theorems. In this way they develop an ownership of the material and experience the excitement of discovering mathematics. The latest version of Sketchpad features enhancements such as built-in web integration, improved sample explorations, and manipulation of functions that make it an effective learning environment in a greater variety of classes.