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  2. Equidiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Equidiagonal_quadrilateral

    A quadrilateral is equidiagonal if and only if [5]: p.19, [4]: Cor.4 K = m n . {\displaystyle \displaystyle K=mn.} This is a direct consequence of the fact that the area of a convex quadrilateral is twice the area of its Varignon parallelogram and that the diagonals in this parallelogram are the bimedians of the quadrilateral.

  3. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite ...

  4. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    Note 2: In a kite, one diagonal bisects the other. The most general kite has unequal diagonals, but there is an infinite number of (non-similar) kites in which the diagonals are equal in length (and the kites are not any other named quadrilateral).

  5. Square - Wikipedia

    en.wikipedia.org/wiki/Square

    There are 2 dihedral subgroups: Dih 2, Dih 1, and 3 cyclic subgroups: Z 4, Z 2, and Z 1. A square is a special case of many lower symmetry quadrilaterals: A rectangle with two adjacent equal sides; A quadrilateral with four equal sides and four right angles; A parallelogram with one right angle and two adjacent equal sides; A rhombus with a ...

  6. Congruence (geometry) - Wikipedia

    en.wikipedia.org/wiki/Congruence_(geometry)

    AAS (angle-angle-side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180°.

  7. Rhombic triacontahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_triacontahedron

    The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 arctan(⁠ 1 / φ ⁠) = arctan(2), or approximately 63.43°. A rhombus so obtained is called a golden rhombus.

  8. Diagonal - Wikipedia

    en.wikipedia.org/wiki/Diagonal

    The diagonals of a cube with side length 1. AC' (shown in blue) is a space diagonal with length , while AC (shown in red) is a face diagonal and has length .. In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

  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.

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