Medians, Perpendicular Bisectors and Altitudes of a Triangle
Shown below are a triangle and its medians, altitudes and perpendicular bisectors. The black segments are the medians, the red lines are the perpendicular bisectors and the purple lines are the altitudes. You have previously learned that each of these special segments are concurrent. What do you now notice about the points of concurrency of this triangle. Move each of the vertices around. Is your original observation still true? Does it matter if the triangle is acute, right or obtuse?
Write a statement that will always be true about the medians, perpendicular bisectors and altitudes of any triangle.