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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 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]
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.
The rhombus has a square as a special case, and is a special case of a kite and parallelogram.. In plane Euclidean geometry, a rhombus (pl.: rhombi or rhombuses) is a quadrilateral whose four sides all have the same length.
An example of a quadrilateral that cannot be tangential is a non-square rectangle. ... completes the proof of the result. ... quadrilateral is a rhombus if and only ...
To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral. The construction shows that the parallelogram is a rhombus, which is equivalent to showing that the sums of the radii of the incircles tangent to each diagonal are equal.
A quadrilateral (a four-sided polygon in the Euclidean plane) is a square if and only if it is any one of the following: A rectangle with four equal sides [1] A rhombus with a right angle between a pair of adjacent sides [1] A rhombus with all angles equal [1] A parallelogram with one right angle and two adjacent equal sides [1]
A quadrilateral is equidiagonal if and only if [5]: p.19, [4]: Cor.4 =. 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.