Triangle Centers Section 5-1 Part B

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

Centroid  The centroid is formed by the intersection of the medians of a triangle. The centroid is the center of gravity. 2x x

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. 2x x

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 AB C

Circumcenter Theorem  The circumcenter is equidistant from the 3 vertices. P AB C

Orthocenter  The orthocenter is formed by the intersection of the 3 altitudes.

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

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

Incenter Theorem  The incenter of a triangle is equidistant from each side of the triangle.

Joke Time  What be a pirate afraid of?  The Daaaaarrrrrrrrrrrrk!

 What be a pirate’s favorite class?  Arrrrrrrrrrrrrrrrrrrrt

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