Van Aubel's Theorem states that if a square is erected outward on each side of an arbitrary quadrilateral, then the two line segments connecting the centers of opposite squares are equal in length and perpendicular to each other. Named for Henricus van Aubel, it is a classical result of Euclidean geometry generalizing simpler square-based constructions on triangles to arbitrary quadrilaterals.
Facts
StatementFor squares constructed on the sides of a quadrilateral, the two line segments between the centers of opposite squares are equal in length and at right angles to one another. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Van Aubel's theorem (Wikipedia)
Sources
1. Van Aubel's theorem (Wikipedia)
Opening paragraph
the two line segments between the centers of opposite squares are of equal lengths and are at right angles to one another.
Attribution paragraph
who published it in 1878.
In Branch: Geometry, Lead sentence
In plane geometry, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral.
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