circumcenter, incenter, centroid, orthocenter

1. Obj. 22 Triangle Segments
The student is able to (I can):
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•
•
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Identify the circumcenter and incenter of a triangle
Identify altitudes and medians of triangles
Identify the orthocenter and centroid of a triangle
Use triangle segments to solve problems

2. circumcenter
The intersection of the perpendicular
bisectors of a triangle.

3. circumcenter
The intersection of the perpendicular
bisectors of a triangle.
It is called the circumcenter, because it is
the center of a circle that circumscribes
the triangle (all three vertices are on the
circle).

4. incenter
The intersection of the angle bisectors of a
triangle.

5. incenter
The intersection of the angle bisectors of a
triangle.
It is called the incenter because it is the
center of the circle that is inscribed in the
circle (the circle just touches all three
sides).

6. median
A segment whose endpoints are a vertex of
the triangle and the midpoint of the
opposite side.
altitude
A perpendicular segment from a vertex to
the line containing the opposite side.

7. centroid
The intersection of the medians of a
triangle. It is also the center of mass for
the triangle.

8. Centroid Theorem
The centroid of a triangle is located
of the distance from each vertex to
the midpoint of the opposite side.
2
3
H
X
G
2
GR = GY
3
Y
R
Z
2
HR = HZ
3
J
2
JR = JX
3

9. orthocenter
The intersection of the altitudes of a
triangle.