Balancing the Triangular Totter

A teeter totter is balanced at a pivot point called its center of mass.

If two people have exactly the same mass, then where would a playground teeter totter’s center of mass lie? Why?

If there were three people on a teeter totter in the shape of a equilateral triangle, where would the center of mass lie? For simplicity, assume the three people have same mass.

What if the teeter totter is an isosceles triangle? Explain why your results would be the same or different.

What if the teeter totter is a scalene triangle? Explain why your results would be the same or different.

Extension
Consider the following centers of triangles. Which one do you think corresponds to the “center of mass“? Explain why. (Hint: The center of mass must always remain inside the triangle. So, make sure you explore the location of each center for various shapes of triangles.)

• The orthocenter of a triangle is the common intersection of the three lines containing the altitudes. An altitude is a perpendicular segment from a vertex to the line of the opposite side. (Note: The foot of the perpendicular may be on the extension of the side of the triangle.)
• The centroid of a triangle is the common intersection of the three medians. A median of a triangle is the segment from a vertex to the midpoint of the opposite side.
• The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle. Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, the circumcenter lies on the perpendicular bisector of each side of the triangle (i.e., where the three perpendicular bisectors intersect).
• The incenter of a triangle is the point in the interior of the triangle that is equidistant from the three sides. Since a point interior to an angle that is equidistant from the two sides of the angle lies on the angle bisector, then the incenter must be on the angle bisector of each angle of the triangle.