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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. Concurrent lines - Wikipedia

    en.wikipedia.org/wiki/Concurrent_lines

    In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors: A triangle's altitudes run from each vertex and meet the opposite side at a right angle. The point where the three altitudes meet is the orthocenter.

  6. 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.)

  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'.

  8. 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.

  9. Perpendicular - Wikipedia

    en.wikipedia.org/wiki/Perpendicular

    The segment AB is perpendicular to the segment CD because the two angles it creates (indicated in orange and blue) are each 90 degrees. The segment AB can be called the perpendicular from A to the segment CD, using "perpendicular" as a noun. The point B is called the foot of the perpendicular from A to segment CD, or simply, the foot of A on CD ...

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