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The square has Dih 4 symmetry, order 8. 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 ...
A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8] A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. [9]
A convex quadrilateral is equidiagonal if and only if its Varignon parallelogram, the parallelogram formed by the midpoints of its sides, is a rhombus.An equivalent condition is that the bimedians of the quadrilateral (the diagonals of the Varignon parallelogram) are perpendicular.
In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus. A rhombus is a tangential quadrilateral. [10] That is, it has an inscribed circle that is tangent to all four sides. A rhombus.
Each has an axis of symmetry parallel to and equidistant from a pair of opposite sides, and another which is the perpendicular bisector of those sides, but, in the case of the crossed rectangle, the first axis is not an axis of symmetry for either side that it bisects. Quadrilaterals with two axes of symmetry, each through a pair of opposite ...
Follow the quadrilateral vertices in the same sequential direction and construct each square on the left hand side of each side of the given quadrilateral. The segments joining the centers of the squares constructed externally (or internally) to the quadrilateral over two opposite sides have been referred to as Van Aubel segments.
A Saccheri quadrilateral is a quadrilateral with two sides of equal length, both perpendicular to a side called the base. The other two angles of a Saccheri quadrilateral are called the summit angles and they have equal measure. The summit angles of a Saccheri quadrilateral are acute if the geometry is hyperbolic, right angles if the geometry ...
A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram). A square is a limiting case of both a kite and a rhombus. Orthodiagonal quadrilaterals that are also equidiagonal quadrilaterals are called midsquare quadrilaterals. [2]