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  2. Varignon's theorem - Wikipedia

    en.wikipedia.org/wiki/Varignon's_theorem

    An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. 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 ...

  3. Euler's quadrilateral theorem - Wikipedia

    en.wikipedia.org/wiki/Euler's_quadrilateral_theorem

    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 .

  4. British flag theorem - Wikipedia

    en.wikipedia.org/wiki/British_flag_theorem

    Even more generally, if the sums of squares of distances from a point P to the two pairs of opposite corners of a parallelogram are compared, the two sums will not in general be equal, but the difference between the two sums will depend only on the shape of the parallelogram and not on the choice of P. [5]

  5. 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 ...

  6. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    Given a convex quadrilateral, the following properties are equivalent, and each implies that the quadrilateral is a trapezoid: It has two adjacent angles that are supplementary, that is, they add up to 180 degrees. The angle between a side and a diagonal is equal to the angle between the opposite side and the same diagonal.

  7. File talk:Euler diagram of quadrilateral types.svg - Wikipedia

    en.wikipedia.org/wiki/File_talk:Euler_diagram_of...

    (Since the diagram is designed to avoid that situation, this means that there is no shape available other than the ones already defined inside the given shape, or in the words of User:Spheniscine above, that the region between the given shape and the shapes it contains is empty.) This is already the case for the name "Rectangle", which is ...

  8. What do people regret the most when they retire? [Video] - AOL

    www.aol.com/finance/people-regret-most-retire...

    Nearly 3 in 10 retirees started receiving benefits at age 62, which is the earliest age possible, resulting in a much-reduced benefit. Only a slim fraction, 4%, of retirees waited until age 70.

  9. Orthodiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Orthodiagonal_quadrilateral

    The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides; that is, the kites are the tangential orthodiagonal quadrilaterals. [1] A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram).