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A simple (non-self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true: [2] [3] Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure. The diagonals bisect each other.
In a Hanner polytope, every two opposite facets are disjoint, and together include all of the vertices of the polytope, so that the convex hull of the two facets is the whole polytope. [ 6 ] [ 7 ] As a simple consequence of this fact, all facets of a Hanner polytope have the same number of vertices as each other (half the number of vertices of ...
Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. 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.
Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length. Parallelogram: a quadrilateral with two pairs of ...
The areas S and T of some two opposite triangles of the four triangles formed by the diagonals satisfy the equation = +, where K is the area of the quadrilateral. [16]: Thm.8 The midpoints of two opposite sides of the trapezoid and the intersection of the diagonals are collinear. [16]: Thm.15
The two line segments connecting opposite points of tangency have equal length. The tangent lengths, distances from a point of tangency to an adjacent vertex of the quadrilateral, are equal at two opposite vertices of the quadrilateral. (At each vertex, there are two adjacent points of tangency, but they are the same distance as each other from ...
In geometry, Hesse's theorem, named for Otto Hesse, states that if two pairs of opposite vertices of a quadrilateral are conjugate with respect to some conic, then so is the third pair. A quadrilateral with this property is called a Hesse quadrilateral .
The two bimedians of a quadrilateral (segments joining midpoints of opposite sides) and the line segment joining the midpoints of the diagonals are concurrent and are all bisected by their point of intersection. [3]: p.125 In a tangential quadrilateral, the four angle bisectors concur at the center of the incircle. [4]