The centroid is twice as close to the midpoint of any one side as it is to the opposite vertex. The three medians intersect each other at a point which is called the centroid of the triangle, which is its center of mass if it has uniform density thus any line through a triangle's centroid and one of its vertices bisects the opposite side. The tangent to a parabola at any point bisects the angle between the line joining the point to the focus and the line from the point and perpendicular to the directrix.īisectors of the sides of a polygon Triangle Medians Įach of the three medians of a triangle is a line segment going through one vertex and the midpoint of the opposite side, so it bisects that side (though not in general perpendicularly). Main article: Parabola § Tangent bisection property ![]() These are the internal angle bisectors at two opposite vertex angles, the external angle bisectors (supplementary angle bisectors) at the other two vertex angles, and the external angle bisectors at the angles formed where the extensions of opposite sides intersect. The excenter of an ex-tangential quadrilateral lies at the intersection of six angle bisectors. In the latter case the quadrilateral is a tangential quadrilateral.Įach diagonal of a rhombus bisects opposite angles. The internal angle bisectors of a convex quadrilateral either form a cyclic quadrilateral (that is, the four intersection points of adjacent angle bisectors are concyclic), or they are concurrent. ![]() There exist integer triangles with a rational angle bisector. ![]() No two non-congruent triangles share the same set of three internal angle bisector lengths. In classical geometry, the bisection is a simple compass and straightedge construction, whose possibility depends on the ability to draw arcs of equal radii and different centers: Construction by straight edge and compass
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