Points of Concurrency
Incenter
Circumcenter
Centroid
Orthocenter
Formed by
intersection
of:
Angle Bisectors
Perpendicular
Bisectors
Medians
Altitudes
Definition of
segments
At each vertex,
bisects angle into two
≅ parts.
Bisects a side into two
≅ parts and forms a
90° angle.
Connects a vertex to
midpoint of the
opposite side.
Location
Always
Inside
• Inside (Acute ∆)
• ON (Right ∆- at
midpoint of hypotenuse)
Always
Inside
• Outside (Obtuse ∆)
Segments ARE
NOT always …
Special
properties:
o passing through
midpoint of
opposite side.
o perpendicular
(90°) to opposite
side.
 equidistant from
the sides of the
∆.
 center of the
inscribed circle.
o angle bisectors.
 equidistant from
the vertices of
the ∆.
 center of
circumscribed
circle.
o angle bisectors.
o perpendicular
(90°) to opposite
side.
 located
Connects a vertex at
90° (perpendicular) to
opposite side (or
extension of).
• Inside (Acute ∆)
• ON (Right ∆- at
vertex of right angle)
• Outside (Obtuse ∆)
o angle bisectors.
o passing through
midpoint of
opposite side.
2
the
3
distance from
vertex to side.
 2:1 ratio from
vertex.
 center of gravity
of ∆.
 NOTHING!
Incenter
Circumcenter
Centroid
Orthocenter
C
A
Drawing /
Picture
(acute ∆)
C
Incenter
E
Circumcenter
C
E
F
(right ∆)
C
E
A
D
D
B
Centroid
F
Circumcenter
A
F
D
(obtuse ∆)
Incenter
E
BB
C
F
C
C
Circumcenter
E
E
D
D
A
B
Centroid
D
F
A
F
B
A
F
C
B
Orthocenter
Special ∆s,
special
properties:
C
F
B E
Orthocenter
B
A
C
E
B
C
D
A
E
BB
A
E
Incenter
Orthocenter
F
C
F
B
B
A
D
F
Centroid
D
A
D
D
E
F
D
BB
A
Equilateral ∆s: All 4 points are located at the same point.
Isosceles ∆s: All 4 points are collinear.
E