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  2. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    The centers of four squares all constructed either internally or externally on the sides of a parallelogram are the vertices of a square. [8] If two lines parallel to sides of a parallelogram are constructed concurrent to a diagonal, then the parallelograms formed on opposite sides of that diagonal are equal in area. [8]

  3. Parallelogon - Wikipedia

    en.wikipedia.org/wiki/Parallelogon

    Parallelogons have an even number of sides and opposite sides that are equal in length. A less obvious corollary is that parallelogons can only have either four or six sides; [1] Parallelogons have 180-degree rotational symmetry around the center. A four-sided parallelogon is called a parallelogram.

  4. Parallelepiped - Wikipedia

    en.wikipedia.org/wiki/Parallelepiped

    a hexahedron with three pairs of parallel faces, a polyhedron with six faces , each of which is a parallelogram, and; a prism of which the base is a parallelogram. The rectangular cuboid (six rectangular faces), cube (six square faces), and the rhombohedron (six rhombus faces) are all special cases of parallelepiped.

  5. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    A rhombus has an axis of symmetry through each pair of opposite vertex angles, while a rectangle has an axis of symmetry through each pair of opposite sides. The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length. The figure formed by joining the midpoints of the sides of a rhombus is a ...

  6. Theorem of the gnomon - Wikipedia

    en.wikipedia.org/wiki/Theorem_of_the_gnomon

    The theorem of the gnomon can be used to construct a new parallelogram or rectangle of equal area to a given parallelogram or rectangle by the means of straightedge and compass constructions. This also allows the representation of a division of two numbers in geometrical terms, an important feature to reformulate geometrical problems in ...

  7. 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.

  8. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into () or ⁠ 1 / 2 ⁠ m(m − 1) parallelograms. These tilings are contained as subsets of vertices, edges and faces in orthogonal projections m-cubes. [7]

  9. 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.