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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^'.

The extremities of parallel radii of two circles are called homologous with respect to the similitude center collinear with them.

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

Two similar figures with parallel homologous lines and connectors of homologous points concurrent at the homothetic center are said to be in homothetic position. If two ...

Nonconcurrent triangles with parallel sides are always homothetic. Homothetic triangles are always perspective triangles. Their perspector is called their homothetic center.

Two figures are said to be similar when all corresponding angles are equal, and are inversely similar when all corresponding angles are equal and described in the opposite ...

A two-dimensional planar closed surface L which has a mass M and a surface density sigma(x,y) (in units of mass per areas squared) such that M=int_Lsigma(x,y)dxdy. The center ...

Given the center of a circle, divide the circle into four equal arcs using a compass alone (a Mascheroni construction).

The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) are x^_ = ...

Given a rectangle BCDE, draw EF=DE on an extension of BE. Bisect BF and call the midpoint G. Now draw a semicircle centered at G, and construct the extension of ED which ...