Search results
Results from the WOW.Com Content Network
A simple (non-self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following: [6] [7] a parallelogram in which a diagonal bisects an interior angle; a parallelogram in which at least two consecutive sides are equal in length; a parallelogram in which the diagonals are perpendicular (an orthodiagonal parallelogram)
The midpoints of the sides of any quadrilateral (convex, concave or crossed) are the vertices of a parallelogram called the Varignon parallelogram. It has the following properties: Each pair of opposite sides of the Varignon parallelogram are parallel to a diagonal in the original quadrilateral.
Two clusters of faces of the bilunabirotunda, the lunes (each lune featuring two triangles adjacent to opposite sides of one square), can be aligned with a congruent patch of faces on the rhombicosidodecahedron. If two bilunabirotundae are aligned this way on opposite sides of the rhombicosidodecahedron, then a cube can be put between the ...
[25] [26] (Thus, for example, if a square is deformed into a rhombus it remains tangential, though to a smaller incircle). If one side is held in a fixed position, then as the quadrilateral is flexed, the incenter traces out a circle of radius / where a,b,c,d are the sides in sequence and s is the semiperimeter.
That is, there exists a circle that is tangent to all four sides. Additionally, if a convex kite is not a rhombus, there is a circle outside the kite that is tangent to the extensions of the four sides; therefore, every convex kite that is not a rhombus is an ex-tangential quadrilateral.
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem .
Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled.. The terms "rhomboid" and "parallelogram" are often erroneously conflated with each other (i.e, when most people refer to a "parallelogram" they almost always mean a rhomboid, a specific subtype of parallelogram); however, while all rhomboids ...
Another area formula, for two sides B and C and angle θ, is K = B ⋅ C ⋅ sin θ . {\displaystyle K=B\cdot C\cdot \sin \theta .\,} Provided that the parallelogram is not a rhombus, the area can be expressed using sides B and C and angle γ {\displaystyle \gamma } at the intersection of the diagonals: [ 9 ]