The centroid is the single point at which the three medians, angle bisectors, and altitudes of a triangle intersect.
Medians: A triangle’s median joins a vertex to the opposite side’s midpoint. At the centroid of a triangle, the three medians agree.
Angle bisectors: An angle bisector splits a triangle’s angle into two equal-measure angles. At the centroid, a triangle’s three angle bisectors agree.
Altitudes: A line drawn perpendicularly from a vertex to the line that contains the opposite side is a triangle’s altitude. At the centroid, a triangle’s three altitudes agree.
Consequently, in a triangle, the altitudes, angle bisectors, and medians are all concurrent.
The centroid is the single point at which the three medians, angle bisectors, and altitudes of a triangle intersect.
Medians: A triangle’s median joins a vertex to the opposite side’s midpoint. At the centroid of a triangle, the three medians agree.
Angle bisectors: An angle bisector splits a triangle’s angle into two equal-measure angles. At the centroid, a triangle’s three angle bisectors agree.
Altitudes: A line drawn perpendicularly from a vertex to the line that contains the opposite side is a triangle’s altitude. At the centroid, a triangle’s three altitudes agree.
Consequently, in a triangle, the altitudes, angle bisectors, and medians are all concurrent.