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  2. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    The area of the parallelogram is the area of the blue region, which is the interior of the parallelogram. The base × height area formula can also be derived using the figure to the right. The area K of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles. The area of the ...

  3. Parallelogram law - Wikipedia

    en.wikipedia.org/wiki/Parallelogram_law

    Vectors involved in the parallelogram law. In a normed space, the statement of the parallelogram law is an equation relating norms: ‖ ‖ + ‖ ‖ = ‖ + ‖ + ‖ ‖,.. The parallelogram law is equivalent to the seemingly weaker statement: ‖ ‖ + ‖ ‖ ‖ + ‖ + ‖ ‖, because the reverse inequality can be obtained from it by substituting (+) for , and () for , and then simplifying.

  4. Parallelepiped - Wikipedia

    en.wikipedia.org/wiki/Parallelepiped

    In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. [a] Three equivalent definitions of parallelepiped are a hexahedron with three pairs of parallel faces,

  5. Pappus's area theorem - Wikipedia

    en.wikipedia.org/wiki/Pappus's_area_theorem

    The extended parallelogram sides DE and FG intersect at H. The line segment AH now "becomes" the side of the third parallelogram BCML attached to the triangle side BC, i.e., one constructs line segments BL and CM over BC, such that BL and CM are a parallel and equal in length to AH.

  6. 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.

  7. Euler's quadrilateral theorem - Wikipedia

    en.wikipedia.org/wiki/Euler's_quadrilateral_theorem

    If the quadrilateral is a parallelogram, then the midpoints of the diagonals coincide so that the connecting line segment has length 0. In addition the parallel sides are of equal length, hence Euler's theorem reduces to + = + which is the parallelogram law.

  8. 9 Items You Should Actually Store In The Freezer, According ...

    www.aol.com/9-items-actually-store-freezer...

    How long: Freeze for up to 6 months, then thaw overnight in the refrigerator before using, Gangeri suggests. Spirits “High-proof spirits are a fun item to keep in your freezer.

  9. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point. The 7th-century Indian mathematician Bhāskara I derived the following formula for the area of a trapezoid with consecutive sides a , c , b , d :