Van_Aubel

Collignon, Van Aubel theorem

Construct squares on the sides of a quadrangle DEFG. The segments UV and SW, joining opposite centers of the squares, as shown, are equal and orthogonal to each other.

Consider the middle T of the diagonal DF. Segments WT and UT are equal and orthogonal, since their doubles in length and parallels: QF and PD are also equal and orthogonal. Later because triangles QGF and DGP are equal, resulting by a pi-rotation about G.
It follows that WTS and UTV are equal, resulting by a pi-rotation about T.
For other properties and proofs look at: Van_Aubel2.html .

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