bisectrices

The bisectrices of the triangle meet at a single point inside it.

Definition

1. Noun (plural form of ):
   • Geometry: In mathematics, "bisectrices" are lines that divide an angle into two equal parts. This is the plural form of bisectrix, which is a less common synonym for bisector.
   • Usage note: The singular bisectrix is rare in modern English; the standard term is bisector (plural: bisectors). "Bisectrices" is used primarily in specialized or historical mathematical contexts, especially in languages like French or Spanish, but it appears in English dictionaries as an irregular plural.

Usage Examples

• Noun:
  • The geometry problem required drawing the bisectrices of each angle in the triangle. (The lines that cut the angles into two equal halves.)
  • In the diagram, the bisectrices intersect at the incenter of the polygon. (The lines that divide angles meet at a central point.)

Advanced Usage

• "Bisectrices of a triangle": The three lines from each vertex that divide the interior angles into two equal parts; they meet at the incenter.

  • The bisectrices of an equilateral triangle are also medians and altitudes. (All three lines coincide in a special case.)

• "Angle bisectrices": A phrase used to specify that these lines refer to angle division, not line segment division.

  • The angle bisectrices of a quadrilateral are not always concurrent. (They do not necessarily meet at a single point.)

Variants and Related Words

• Bisector (n): the standard modern term for a line that divides an angle or a line segment into two equal parts.

  • Draw the perpendicular bisector of the segment. (The line that divides the segment into two equal parts at a right angle.)

• Bisect (v): to divide into two equal parts.

  • The line bisects the angle perfectly. (It cuts the angle into two equal halves.)

• Bisection (n): the act or process of dividing into two equal parts.

  • The bisection of the angle was done with a compass and straightedge. (The action of dividing the angle.)

Synonyms

• Angle bisector: the exact synonym for a line that divides an angle into two equal parts.

  • The angle bisector of a 60-degree angle creates two 30-degree angles. (The line performs the division.)

• Bisecting line: a general term for any line that cuts something into two equal parts.

  • The bisecting line of the angle is drawn from the vertex. (The line originating at the angle's vertex.)

Related Idioms

• "Bisectrices of a circle" (rare): a phrase used in some older texts to refer to diameters that divide the circle into two equal halves, though this is not standard terminology.
  • The bisectrices of a circle are its diameters. (Lines through the center dividing the circle.)

Note: "Bisectrices" is an irregular plural form (from Latin) and is not commonly used in everyday English mathematics. The standard term is "bisectors." This word appears in historical or multilingual contexts, especially when translating from Romance languages.