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  2. Bisection - Wikipedia

    en.wikipedia.org/wiki/Bisection

    An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle. The 'interior' or 'internal bisector' of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles.

  3. Angle bisector theorem - Wikipedia

    en.wikipedia.org/wiki/Angle_bisector_theorem

    Consider a triangle ABC.Let the angle bisector of angle ∠ A intersect side BC at a point D between B and C.The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC:

  4. Perpendicular bisector construction of a quadrilateral

    en.wikipedia.org/wiki/Perpendicular_bisector...

    The perpendicular bisector construction can be reversed via isogonal conjugation. [3] That is, given (+) ... be the angles of (). For every , the ratio ...

  5. Thales's theorem - Wikipedia

    en.wikipedia.org/wiki/Thales's_theorem

    The locus of points equidistant from two given points is a straight line that is called the perpendicular bisector of the line segment connecting the points. The perpendicular bisectors of any two sides of a triangle intersect in exactly one point. This point must be equidistant from the vertices of the triangle.)

  6. Concurrent lines - Wikipedia

    en.wikipedia.org/wiki/Concurrent_lines

    The perpendicular bisectors of all chords of a circle are concurrent at the center of the circle. The lines perpendicular to the tangents to a circle at the points of tangency are concurrent at the center. All area bisectors and perimeter bisectors of a circle are diameters, and they are concurrent at the circle's center.

  7. Constructions in hyperbolic geometry - Wikipedia

    en.wikipedia.org/wiki/Constructions_in...

    Bisect one of the angles made by these two lines and name the angle bisector b. Using a hyperbolic ruler, construct a line c such that c is perpendicular to b and parallel to a. As a result, c is also parallel to a', making c the common parallel to lines a and a'. [3] Case 2: a and a' are parallel to each other

  8. Kite (geometry) - Wikipedia

    en.wikipedia.org/wiki/Kite_(geometry)

    One diagonal crosses the midpoint of the other diagonal at a right angle, forming its perpendicular bisector. [9] (In the concave case, the line through one of the diagonals bisects the other.) One diagonal is a line of symmetry. It divides the quadrilateral into two congruent triangles that are mirror images of each other. [7]

  9. Incenter - Wikipedia

    en.wikipedia.org/wiki/Incenter

    A line that is an angle bisector is equidistant from both of its lines when measuring by the perpendicular. At the point where two bisectors intersect, this point is perpendicularly equidistant from the final angle's forming lines (because they are the same distance from this angles opposite edge), and therefore lies on its angle bisector line.