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5.1 bisectors of triangles (unnamed (Incenter, Vertex to circumcenter are…
5.1 bisectors of triangles
vocab:
concurrent : A set of lines or curves are said to be concurrent if they all intersect. at the same point. In the figure below, the three lines are concurrent because they all intersect at a single point P.
locus:a curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions
incenter: is the center of the incircle for a polygon or insphere for a polyhedron (when they exist)
angle bisector theorem: is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle.
obtuse triangle
Outside
acute triangle
Inside
right angle
On Hypotenuse
Vertex to circumcenter are congruent
Sides are bisected
Angles are not bisected
Perpendicular lines are not congruent
Circumcenter
Incenter
Vertex to circumcenter are not congruent
Sides are not bisected
Angles are bisected
