Triangles and Medians

By

Jeffrey R. Frye

This write up covers the topics posed in problems 1 and2.  The relationships betweenoriginal triangles and the triangles formed by the medians of these trianglesis discussed and explored by using GSP. The area relationship between the new median formed triangle and theoriginal triangle is 3/4.

By comparing the areas of the triangles, the relationship between the triangle formed by the medians and the original triangle appears to remain a ratio of 3/4.  Theactual calculations done by GSP are shown.  If the original triangles are equilateral, then thesubsequent triangles formed by the medians will also be equilateral.  If the original triangles are isosceles,then the subsequent triangles will also be isosceles.  If the original triangles are right triangles, the nexttriangle formed by the medians will not be right, but the following oneconstructed by the new medians will be a right triangle.  This alternating pattern holds forright triangles.  I used GSPconstruction to explore and found this pattern to hold for the classificationsof triangles mentioned.  These areexamples of the different triangles that were constructed.