If you covered the Pythagoras theorem, you could prove that the small triangles having altitudes as catheti and the common side as a hypotenuse are equal.
Triangle area is
If two sides are equal, then the altitudes of the 3rd vertex above them must also be equal.
If no two altitudes are equal, no two sides can be equal.
if you begin with "at least 2 acute angles are equal", you can use the Sine Rule