Cleaver (geometry)
Encyclopedia
In geometry
, a cleaver of a triangle
is a line segment
that bisect
s the perimeter
of the triangle and has one endpoint at the midpoint of one of the three sides.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a cleaver of a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
is a line segment
Line segment
In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment...
that bisect
Bisect
Bisection is the general activity of dividing something into two equal parts.Bisect may mean:*bisection, in geometry, dividing something into two equal parts* bisection of earthworms to study regeneration...
s the perimeter
Perimeter
A perimeter is a path that surrounds an area. The word comes from the Greek peri and meter . The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circular area is called circumference.- Practical uses :Calculating...
of the triangle and has one endpoint at the midpoint of one of the three sides.
- Each cleaver is parallel to one of the angle bisectors of the triangle.
- The three cleavers concurConcurrent linesIn geometry, two or more lines are said to be concurrent if they intersect at a single point.In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors:...
at that center of the Spieker circleSpieker circleIn geometry, the incircle of the medial triangle of a triangle ABC is the Spieker circle. Its center, the Spieker center, is the center of mass of the boundary of triangle ABC as well as being the incenter of the medial triangle....
.