Prove or disprove by giving a counterexample.
If two medians of a triangle are of the same length, 
then the triangle is isosceles.

Proof:
Draw triangle ABC with medians BD and CE, and label 
their point of intersection X (which is the centroid).
Given: Medians BD and CE, and BD = CE
Prove: AB = AC

Statements:

1) Medians BD and CE, and BD = CE
2) BX = (2/3)(BD),
   DX = (1/3)(BD),
   CX = (2/3)(CE), 
   EX = (1/3)(CE)
3) BX = CX, DX = EX
4) Angle BXE = Angle CXD
5) Triangle BXE is congruent to Triangle CXD
6) BE = CD
7) 2(BE) = 2(CD)
8) AB = AC

Reasons:

1) Given
2) The medians of a triangle intersect 
   in a point that is 2/3 of the distance 
   from each vertex to the midpoint of 
   the opposite side.
3) Substitution property
4) Vertical angles are congruent
5) Side-angle-side
6) Corresponding parts of congruent triangles
   are congruent
7) Multiplication property of equality 
8) Midpoint theorem

Edwin