Imagine two triangles, \(ABC\) and \(DEF\), such that the length of lines \(AB\) and \(DE\) are equal, the length of lines \(BC\) and \(EF\) are equal and the angles \(ABC\) and \(DEF\) are equal:
Since line \(AB\) has the same length as \(DE\), then we can lay triangle \(ABC\) on top of \(DEF\) such that line \(AB\) exactly covers the line \(DE\). Since angles \(ABC\) and \(DEF\) are equal, and lines \(AB\) and \(DE\) have equal length, then the line \(BC\) would exactly covers the line \(EF\):
This shows that we can put one triangle one top of another such that points \(A\), \(B\) and \(C\) are in the exact same position as points \(D\), \(E\) and \(F\), but if that's the case, then lines \(AC\) and \(DF\) must also have equal length:
Also, if it's possible to put points \(A\), \(B\) and \(C\) in the exact same position as points \(D\), \(E\) and \(F\), the angles \(BAC\) and \(EDF\) should be equal. Similarly, angles \(ACB\) and \(DFE\) should also be equal.