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παραλληλόγραμμον: Difference between revisions
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[[File:Parallelogram.svg|thumb|Parallelogram|alt=Parallelogram.svg]] | |wketx=[[File:Parallelogram.svg|thumb|Parallelogram|alt=Parallelogram.svg]] | ||
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. | In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. | ||
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|ptext=[[https://www.translatum.gr/images/pape/pape-02-0488.png Seite 488]] τό, das Parallelogramm, eine Figur, die von vier Linien eingeschlossen ist, deren zwei und zwei einander gleichlaufen, Euclid. u. A. – Adjectivisch bei Plut. adv. Stoic. 39, wie [[παραλληλόγραμμον]] [[σχῆμα]] Strab. | |ptext=[[https://www.translatum.gr/images/pape/pape-02-0488.png Seite 488]] τό, das Parallelogramm, eine Figur, die von vier Linien eingeschlossen ist, deren zwei und zwei einander gleichlaufen, Euclid. u. A. – Adjectivisch bei Plut. adv. Stoic. 39, wie [[παραλληλόγραμμον]] [[σχῆμα]] Strab. | ||
