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triangle centers A triangle has more than one center Believe it or not, there are four common ways of finding the "center" of a triangle. 1 CENTROID The centroid is the intersection of all three medians (lines from the midpoint of a side to the opposite vertex). A Midpoint of AC All three intersect at the centroid. Midpoint of AB These lines are called MEDIANS--they chop the area of the triangle in two. C B Midpoint of BC 2 ORTHOCENTER The orthocenter is the intersection of the altitudes drawn on all three sides. A Altitude on AC Altitude on AB Altitudes go from a vertex to meet the opposite side, and are perpendicular to that side. C Altitude on BC B 3 INCENTER The incenter is the center of the biggest circle you can draw inside the triangle. A line from the incenter to a vertex exactly bisects the angle at that vertex. Draw a circle inside which just touches all three sides. "incircle" Incenter is center of the "incircle." 182 Chapter 4