Medians of a triangle and similar triangle properties
Prove using similar triangle properties that "any two medians of a triangle divide each other in the ratio $2:1$. I do not know which criteria of similar triangle must be used
Here's a diagram:
$|AB|:|ED|=2:1$ and $AB\parallel ED$ (midpoint theorem) $\Longrightarrow \triangle ABC \sim \triangle EDC$.
Now use alternate interior angles to prove $\triangle ABS \sim \triangle DES$. Use the fact that $|AB|:|ED|=2:1$ to conclude.