Angle Bisector Theorems and Problems- Table of Content

Euclid's Elements Book I, 23 Definitions. One-page visual illustration. Angles and more.
Euclid's Elements Book. Index.

Book I, Proposition 9: Bisect a given angle.
Construction of angle bisector

Centroid /Barycenter. Index.
Angle bisectors

Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem

Journey to the Center of a Triangle (1976). Incenter (Angle bisectors), Circumcenter, Centroid, Orthocenter.

Animated illustration of the celebrated Morley's angle trisector theorem 

Morley's Triangle & Center: Trisection of angles.

Blanchet Theorem. Altitude, Angle Bisector.

Isogonic-Jacobi Theorem: Using TracenPoche Dynamic Geometry Software.
Isogonal conjugate line, reflecting line on the angle bisector

Triangle: Incircle, Perpendicular, Angle Bisector. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition.

Heron's Formula.
Key facts and a purely geometric step-by-step proof.
Geometry help: Key Facts: Angle bisector. Preliminary propositions 

Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.

Proposed Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

Proposed Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence.

Proposed Problem 377.
Triangle, Internal Angle Bisector, Altitude.

Proposed Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors.

Proposed Problem 375.
Triangle, Excenter, External Angle Bisectors.

Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors.

Proposed Problem 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.

Proposed Problem 340.
Triangle, Angle Bisectors, Perpendiculars, Distances. Exterior Point.

Proposed Problem 339.
Triangle, Angle Bisectors, Perpendiculars, Distances. Interior Point.

Proposed Problem 338.
Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points.

Proposed Problem 337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points.

Proposed Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.

Proposed Problem 216. Quadrilateral, Angle Bisectors, and Concurrency.

Proposed Problem 215. Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral.

Sangaku Problem. The incenters of four triangles in a cyclic quadrilateral form a rectangle. Angle bisectors.

Proposed Problem 214. Quadrilateral and Angle Bisectors.

Proposed Problem 187. Right Triangle, Altitude, Incenters, Circles, Angle bisector.  

Proposed Problem 134. Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter.  

Proposed Problem 133. Triangle, Angle Bisectors, Collinear Points.

Triangle with the bisectors of the exterior angles. Collinearity. Key concept: Menelaus Theorem.
 

Proposed Problem 128. Incenter of a Triangle, Angle Bisectors, Sum of Ratios.

Proposed Problem 127. Centroid and Incenter of a Triangle, Parallel, Proportions.

Proposed Problem 126. Incenter of Triangle, Angle Bisector, Proportions.

Proposed Problem 80. Area of a triangle, side, incircle, inradius. Angle bisector.

Proposed Problem 57: Angle bisector, circles Cyclic Quadrilateral.

Proposed Problem 56: Angle bisector, circles Parallel Lines.

Proposed Problem 55: Angle bisector, circles Cyclic Quadrilateral.

Proposed Problem 54: Angle bisector, circles Midpoint of arc.

Proposed Problem 53: Angle bisector, circles

Problem 50. Triangle with Equilateral triangles.

Proposed Problem 40.
Triangle, Incenter, Excenter, Angles 80, 40, Distances. Angle bisector

Proposed Problem 39.
Triangle, Incircle, Bisector, Cyclic Quadrilateral and angles.

Proposed Problem 38.
Right Triangle, altitude, incircles, incenters, and angles. Angle bisector

Proposed Problem 37.
Right Triangle, altitude, incircles, incenters, orthocenter, and angles.

Proposed Problem 35.
Incenters and Inradii in Cyclic Quadrilateral. Angle bisector.

Geometry Online Glossary . Angle bisector and more.
Geometry Glossary based on the new New York State mathematics standards initiative.