Determine the Incenter by using a protractor to draw a circle inside of a triangle. Make the sides of each of the angles in the triangle touch the outer edges of the circle so that the center of the circle marks the Incircle of the triangle. Find the radius of the circle by measuring its diameter (width) across and dividing by two.
Find the Circumcenter of a triangle by drawing a circle around the triangle so that each corner of the triangle touches the inner edge of the circle. The center of the circle where the protractor was drawn from is then the Circumcenter of the triangle. Find the radius of the circle by measuring its diameter across and dividing by two.
Measure for the Centroid by finding the intersecting point of the three medians, which according to the jimloy.com geometry website, are "the lines drawn from the vertices to the bisectors of the opposite sides". In layman's terms, the medians are straight lines drawn inward from each corner (vertex) of the triangle and ending in the center of the opposite sector (hence the "bisector"). The point where the three medians meet is the Centroid marking the center of gravity or mass for the triangle.
Locate the Orthocenter of a triangle by finding the point where the three altitudes of a triangle meet. This measurement probably makes the least sense to the average person because the Orthocenter is often located on the right angle or outside of a triangle. Altitudes are created by drawing a straight line from a vertex to the opposite side of the triangle (the base) forming a right angle. The three altitudes meet at the Orthocenter.