A perimeter-bisecting segment of a polygon originating from the midpoint of one side. Each cleaver , ,
and in a triangle is parallel to an angle
bisector of the triangle (shown as dashed lines above). In addition, the three
cleavers concur in a point known as the cleavance center, which is the Spieker
center, i.e., incenter of the medial
triangle (Honsberger 1995, p. 2).
Avishalom, D. "Perimeter-Bisectors in a Triangle" [Hebrew]. Riveon Lematematika13, 46-49, 1959.Avishalom,
D. "The Perimetric Bisection of Triangles." Math. Mag.36,
60-62, 1963.Honsberger, R. "Cleavers and Splitters." Episodes
in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math.
Assoc. Amer., pp. 1-14, 1995.Jarden, D. "Synthetical Proof
for the Theorem on the Center of Perimeter-Bisectors in a Triangle" [Hebrew].
Riveon Lematematika13, 50, 1959.
, 
,
and 
in a triangle 
is parallel to an angle
bisector of the triangle (shown as dashed lines above). In addition, the three
cleavers concur in a point 
known as the cleavance center, which is the Spieker
center, i.e., incenter of the medial
triangle (Honsberger 1995, p. 2).
