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  2. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    A parallelogram with base b and height h can be divided into a trapezoid and a right triangle, and rearranged into a rectangle, as shown in the figure to the left. This means that the area of a parallelogram is the same as that of a rectangle with the same base and height:

  3. 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.

  4. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    Trapezoid special cases. The orange figures also qualify as parallelograms. A right trapezoid (also called right-angled trapezoid) has two adjacent right angles. [13] Right trapezoids are used in the trapezoidal rule for estimating areas under a curve. An acute trapezoid has two adjacent acute angles on its longer base edge.

  5. Equidiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Equidiagonal_quadrilateral

    A parallelogram is equidiagonal if and only if it is a rectangle, [6] and a trapezoid is equidiagonal if and only if it is an isosceles trapezoid. The cyclic equidiagonal quadrilaterals are exactly the isosceles trapezoids.

  6. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    Trapezia (UK) and trapezoids (US) include parallelograms. Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.

  7. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.

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  9. Missing square puzzle - Wikipedia

    en.wikipedia.org/wiki/Missing_square_puzzle

    Splitting the thin parallelogram area (yellow) into little parts, and building a single unit square with them. The key to the puzzle is the fact that neither of the 13×5 "triangles" is truly a triangle, nor would either truly be 13x5 if it were, because what appears to be the hypotenuse is bent.

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