Definition
Geometric construction
A geometric construction is a sequence of exact steps that creates a figure meeting stated conditions.
Continue from this idea into connected AXIO math.
What it means
A construction is more than a neat sketch. You follow allowed steps so the result has guaranteed properties—for example, equal lengths or a right angle. The tools might be a compass and straightedge, a ruler and protractor, or approved geometry software.
Remember it
Do not draw what looks right; build what must be right.
Example
To construct the perpendicular bisector of segment AB, draw equal-radius arcs from A and B so they cross above and below the segment. Join the two crossings. That line cuts AB in half at a right angle.
Watch for
A freehand line that appears perpendicular is a sketch, not a construction, unless the permitted steps guarantee the right angle.
Common mix-up
The permitted tools are part of the task; compass-and-straightedge construction is one kind, not the only possible kind.
Exact meaning
A geometric construction is a prescribed sequence of geometric operations, using only the tools allowed by the task, that produces a figure satisfying specified geometric properties or relationships.