Triangle Centers

1
Triangle Centers

• Section 5-1 Part B

2

• Unlike squares and circles, triangles have many
  centers. The ancient Greeks found four
  incenter, centroid, circumcenter, and orthocenter.

3
Centroid

• The centroid is formed by the intersection of the
  medians of a triangle.

x
2x
The centroid is the center of gravity.
4
Centroid Theorem

• The centroid of a triangle is located two thirds
  of the distance from a vertex to the midpoint of
  the side opposite the vertex on a median.

x
2x
5
Circumcenter

• The circumcenter is the center of the
  circumcircle and is formed by the intersection of
  the perpendicular bisectors of the sides of a
  triangle.

P
A
B
C
6
Circumcenter Theorem 5.3

• The circumcenter is equidistant from the 3
  vertices.

P
A
B
C
7
Orthocenter

• The orthocenter is formed by the intersection of
  the 3 altitudes.

8
Euler Line

• The Euler line is the line on which the
  orthocenter, centroid, and circumcenter lie.

9
Incenter

• The incenter is the center of the inscribed
  circle and is formed by the intersection of the
  angle bisectors

10
Incenter Theorem

• The incenter of a triangle is equidistant from
  each side of the triangle.

11
Joke Time

• What be a pirate afraid of?
• The Daaaaarrrrrrrrrrrrk!

12

• What be a pirates favorite class?
• Arrrrrrrrrrrrrrrrrrrrt

13

• How much does it cost for a pirate to pierce his
  ears?
• A bucaneer!