construct-geometric-figure

Construct a Geometric Figure

Produce a ruler-and-compass construction for a specified geometric figure, documenting every step with its Euclidean justification and verifying the result against the original specification.

When to Use

• Given specific geometric elements (points, segments, angles) and asked to construct a figure
• Tasked with producing a classical Euclidean construction (bisectors, perpendiculars, tangents)
• Verifying whether a figure is constructible with straightedge and compass alone
• Generating construction instructions for educational or documentation purposes
• Converting a geometric specification into an ordered sequence of primitive operations

Inputs

• Required: Description of the target figure (e.g., "equilateral triangle with side length AB")
• Required: Given elements (points, segments, circles, angles provided as starting data)
• Optional: Output format (narrative prose, numbered steps, pseudocode, SVG coordinates)
• Optional: Level of justification detail (terse, standard, rigorous with theorem citations)
• Optional: Whether to include impossibility analysis if figure is not constructible

Procedure

Step 1: Identify Given Elements and Target Figure

Parse the problem statement to extract:

1. Given elements -- list every point, segment, angle, circle, or length provided.
2. Target figure -- state precisely what must be constructed.
3. Constraints -- note any additional conditions (congruence, parallelism, tangency, collinearity).

Express the problem in standard form:

Given: Points A, B; segment AB; circle C1 centered at A with radius r.
Construct: Equilateral triangle ABC with AB as one side.
Constraints: C must lie on the same side of AB as point P (if specified).

Verify that all referenced elements are well-defined and consistent.

Got: A clear, unambiguous restatement of the construction problem with every given element cataloged and the target figure precisely described.