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parallelogram$57794$ - translation to greek
MATHEMATICAL THEOREM
Parallelogram identity; Parallelogram equation; Parallelogram rule; Parallelogram equality; Parallelogram Law
parallelogram
n. παραλληλόγραμμο
Definition
parallelogram
[par?'l?l?gram]
¦ noun a four-sided plane rectilinear figure with opposite sides parallel.
Origin
C16: from Fr. parallelogramme, via late L. from Gk parallelogrammon, from parallelos 'alongside another' + gramme 'line'.
Wikipedia
Parallelogram law
In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. We use these notations for the sides: AB, BC, CD, DA. But since in Euclidean geometry a parallelogram necessarily has opposite sides equal, that is, AB = CD and BC = DA, the law can be stated as
If the parallelogram is a rectangle, the two diagonals are of equal lengths AC = BD, so
and the statement reduces to the Pythagorean theorem. For the general quadrilateral with four sides not necessarily equal, where is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that for a parallelogram, and so the general formula simplifies to the parallelogram law.