An invesigation of triangles formed by medians of a larger triangle.
by Jamila K. Eagles
We begin this investigation by looking at the case where the original
triangle ABC is an isisceles triangle. In the figure below, we can see that
the triangle formed by its medians is also an isosceles triangle, since
sides DE and BE are both equal.
Next we want to look at the case where triangle ABC is a right triangle.
It is easy to assume that the triangle formed by its medians is also a right
triangle. Looking at the the figure below, we see that the assumption does
not hold true in this case.
What if the triangle formed by the medians is a right triangle? Will
the original triangle ABC be a a right triangle? In the figure below, We
see that in the case where the triangle formed by medians is a right triangle,
the larger triangle ABC is not a right triangle.
The question now is when are both triangles right triangles? From the
figure below, We know that both triangles will be right triangles when the
other two triangles are 35 and 55 degrees.
