Facts About Quadrilaterals

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A quadrilateral is a polygon with four sides. The origin of the word ‘œquadrilateral’ is from Latin for quad, originating from the Indo-European ‘œkwetwer’ or ‘œquarter’ which means ‘œfour.’ ‘œLateral’ refers to ‘œlatus’ or ‘œside’ in Latin.

Fact 1. The term quadrangle has exactly the same meaning as quadrilateral. However, the two related terms,  complete quadrangle and complete quadrilateral, describe essentially different configurations.

Fact 2.   A quadrilateral may be convex or concave. A quadrilateral that is concave has an angle exceeding 180o. In either case, the quadrilateral is simple, which means that the four sides of the quadrilateral only meet at the vertices, two at a time. Therefore, the two, non-adjacent sides do not cross. A quadrilateral that is not simple is also known as self-intersecting to indicate that a pair of non-adjacent sides intersects.

Fact 3.    A convex (outward) quadrilateral with one pair of parallel sides is known as a trapezoid in the U.S. and a trapezium in other parts of the world. In both instances it comes from a Greek word meaning ‘œa little table.’

Fact 4.  The difference between quadrangle  and quadrilateral is that one emphasizes the fact that the figure has four sides while the other emphasizes the fact that the figure contains four angles.

Fact 5.  The Indian mathematician, Brahmagupta is noted for his theorems on the area of a cyclic quadrilateral and for the lengths of the diagonals with reference to the sides of a quadrilateral. This was documented in the Brahmasphutasiddhanta.

Fact 6. The sum of the interior angles of all quadrilaterals is 360º

Fact 7.  A quadrilateral with one pair of sides parallel is called a trapezium in the U.K. and a trapezoid in the U.S. A quadrilateral with no pair of sides parallel is called a trapezoid in the U.K. and a trapezium in the U.S.

Fact 8.  A skewed quadrilateral is referred to as when the points do not lie in a plane. The types of such topological  quadrilaterals are convex quadrilaterals, concave quadrilaterals,  and crossed quadrilaterals.

Fact 9.  Rectangles are quadrilaterals. The ratio of the purportedly  most pleasing rectangle used as a base by architects and artists is called the golden rectangle. The golden rectangle is formed by drawing a square and partitioning it equally by half. A diagonal line is drawn from the midpoint of the halved portion to the opposite corner. The length of the diagonal line is used as a radius to form a circle. The extended rectangle formed from the arc of the circle is called a golden rectangle.

Fact 10.  It is postulated that Leonardo da Vinci’s ‘œMona Lisa’ was based upon the golden rectangle.

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