<P> In particular, the centroid of a parallelogram is the meeting point of its two diagonals . This is not true for other quadrilaterals . </P> <P> For the same reason, the centroid of an object with translational symmetry is undefined (or lies outside the enclosing space), because a translation has no fixed point . </P> <P> The centroid of a triangle is the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side). It lies on the triangle's Euler line, which also goes through various other key points including the orthocenter and the circumcenter . </P> <P> Any of the three medians through the centroid divides the triangle's area in half . This is not true for other lines through the centroid; the greatest departure from the equal - area division occurs when a line through the centroid is parallel to a side of the triangle, creating a smaller triangle and a trapezoid; in this case the trapezoid's area is 5 / 9 that of the original triangle . </P>

Where is the center of gravity in a triangle