Question 1

  • Construct the three midpoints of the sides of a triangle.
  • Construct the segment connecting the vertices to the midpoints of the sides. 
  • Use the intersect tool and mark the point of concurrency of the 3 medians.
The three segments you have constructed are the medians of the triangle. How are medians different than a perpendicular bisector or angle bisector?

Question 2

The point of concurrency of of the medians is called the centroid or the geometric center of the triangle. Can the centroid be on the triangle or outside the triangle?

Question 3

Measure the distance from the centroid to the vertex of the one of the median. Along the same median, measure the distance from the centroid to the midpoint of the side of the triangle. Is the centroid midpoint of the median? Explain why or why not.

Question 4

Where along the median is the centroid located?

Question 5

What relationship is there between the coordinates of the vertices of the triangle and the centroid.