Module 2 Topic 1 Lesson 5 Activity 5.3
Medians
Construct the three medians of each triangle.
2.
Make a conjecture about the location of the intersection of the three medians of any triangle. Move points A, B, and C around so that you have an acute triangle, an obtuse triangle, a right triangle, and an equilateral triangle. Where is the point of concurrency for the medians in each case?
3a.
Measure the distance from the centroid to each vertex of the triangle. Is the centroid always, sometimes, or never equidistant from each vertex of the triangle. Be certain to test for each type of triangle.
3b.
Measure the perpendicular distance from the centroid to each side of the triangle. Is the centroid always, sometimes, or never equidistant from each side of the triangle. Be certain to test for each type of triangle.
4.
Compare the distance from the centroid to the vertex and the distance from the centroid to the midpoint of the opposite side in each of the triangles. What is the ratio?