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The midpoints of the sides of an arbitrary quadrilateral form a parallelogram. If the quadrilateral is convex or concave (not complex), then the area of the parallelogram is half the area of the quadrilateral. If one introduces the concept of oriented areas for n-gons, then this area equality also holds for complex quadrilaterals. [2]
In any quadrilateral, the four edge midpoints form a parallelogram, the Varignon parallelogram, whose sides are parallel to the diagonals and half their length.It follows that, in an equidiagonal and orthodiagonal quadrilateral, the sides of the Varignon parallelogram are equal-length and perpendicular; that is, it is a square.
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem .
The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides, hence each bisecting two sides. The two bimedians and the line segment joining the midpoints of the diagonals are concurrent at (all intersect at)a point called the "vertex centroid", which is the midpoint of all three of these segments.
A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. [6] A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8]
From January 2008 to December 2012, if you bought shares in companies when F. Duane Ackerman joined the board, and sold them when he left, you would have a 32.0 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A l (half linear dimensions yields quarter area), and the area of the parallelogram is A ...
About This Series “A Path Out Of Trouble” is the fourth in a series of stories about police in schools. It is produced in collaboration with The Hechinger Report.