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  2. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    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 ...

  3. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    When both diagonals bisect another, it's a parallelogram. Ex-tangential quadrilateral: the four extensions of the sides are tangent to an excircle. An equilic quadrilateral has two opposite equal sides that when extended, meet at 60°. A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. [6]

  4. Varignon's theorem - Wikipedia

    en.wikipedia.org/wiki/Varignon's_theorem

    The Varignon parallelogram is a rectangle if and only if the diagonals of the quadrilateral are perpendicular, that is, if the quadrilateral is an orthodiagonal quadrilateral. [6]: p. 14 [7]: p. 169 For a self-crossing quadrilateral, the Varignon parallelogram can degenerate to four collinear points, forming a line segment traversed twice.

  5. Midpoint polygon - Wikipedia

    en.wikipedia.org/wiki/Midpoint_polygon

    The midpoint polygon of a quadrilateral is a parallelogram called its Varignon parallelogram. If the quadrilateral is simple, the area of the parallelogram is one half the area of the original quadrilateral. The perimeter of the parallelogram equals the sum of the diagonals of the original quadrilateral.

  6. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Cyclic quadrilateral. square; kite; Parallelogram. Rhombus (equilateral ... square (regular quadrilateral) Tangential quadrilateral; Trapezoid or trapezium Isosceles ...

  7. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    The quadrilateral is a parallelogram when ... where a is the short base, b is the long base, and c and d are the trapezoid legs.

  8. Parallelogram law - Wikipedia

    en.wikipedia.org/wiki/Parallelogram_law

    For the general quadrilateral (with four sides not necessarily equal) Euler's quadrilateral theorem states + + + = + +, where is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that x = 0 {\displaystyle x=0} for a parallelogram, and so the general formula simplifies to the parallelogram law.

  9. File:Varignon parallelogram.svg - Wikipedia

    en.wikipedia.org/.../File:Varignon_parallelogram.svg

    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 l /4 (half linear dimensions yields quarter area) = A q /2, and the area of the parallelogram is A ...