# Honors Geometry Special Triangle Segments

## 16 terms · really hard stuff that we all need to study

### perpendicular bisector

a line or line segment that passes through the midpoint of a side of a triangle and is perpendicular to that side

### median

a segment that connects a vertex of a triangle to the midpoint of the side opposite that vertex

### altitude

a segment from one vertex of a triangle and perpendicular to the line containing the opposite side of the triangle (may not be inside of the triangle!!)

### angle bisector

a segment that bisects an angle of the triangle and has one endpoint on the side opposite of the bisected angle

### perpendicular bisector theorem

any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment (the converse is also true)

### angle bisector theorem

any point on the bisector of an angle is equidistant from the sides of the angle (the converse is also true)

### circumcenter goes with

with the perpendicular bisector

### incenter goes with

with the angle bisectors

with the median

### orthocenter goes with

with the altitude

### circumcenter

the perpendicular bisectors of the sides of a triangle are concurrent at a point that is equidistant from the vertices

### incenter

the angle bisectors of a triangle are concurrent at a point equidistant from the sides of a triangle

### centroid

the medians of a triangle are concurrent at a point that is two thirds the distance of the median from each vertex

### orthocenter

the lines that contain the altitudes of a triangle are concurrent

### concurrent

when three or more lines intersect in one point

### point of concurrency

the point where concurrent lines meet