We are to investigate the Medial Triangle  a triangle constructed out of the medians of any given triangle. To make life easier on us, let's construct them so they are connected.

The Construction: Given a triangle MKH, if one was to construct a triangle using it's medians, a good construction can be done as follows:

1. Area
So now we have our triangle LKJ. What is the relationship to HMK? Let's look at some givens:
So now we can deduce that HLG is exactly onefourth the area of HLK, making the medial triangle (since all else was similiar) threefourths the area of our original triangle.
2. IsoscelesRight ...
Let's look at a right isosceles triangle ...


We can actually make a square ADEF since triangle ADF is a right isosceles triangle as well.
By this, we get EC congruent to DC (corresponding sides), making EDC an isosceles triangle. But it's not a right one.