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In any triangle, if one of the sides is extended, the exterior angle is greater than both the interior and opposite angles.

A set in R^d formed by translating an affine subspace or by the intersection of a set of hyperplanes.

Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

An arrangement of points with no three collinear, or of lines with no three concurrent.

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

A similarity transformation which preserves orientation, also called a homothety.

The metric ds^2=(dx^2+dy^2)/((1-x^2-y^2)^2) for the Poincaré hyperbolic disk, which is a model for hyperbolic geometry. The hyperbolic metric is invariant under conformal ...

Three concurrent homologous lines pass respectively through three fixed points on the similitude circle which are known as the invariable points.

A bistable eight-sided polyhedron discovered by Wunderlich and Schwabe (1986).