Given $\overline{AB}=c$, $\overline{AC}=b$, $m_a$, construct the triangle $ABC$.
I did the following:
And then used the compass to draw the distances $c,b$:
I've drawn the paralelogram:
After drawing the line segment BC, we have:
Is my construction correct? I've seen other constructions, specially this one from Cut-the-Knot, but it seemed a little bit more advanced (I know next to nothing in geometric constructions, decided to learn some weeks ago). I'm still afraid that that construction is "better" by having some aspect mine doesn't have.
I spent a bit of time stuck trying to construct this because I thought that "given $b,c,m_a$ meant that these could be any lengths. I figured out later that perhaps, this is impossible (due to basic properties of the triangle: If I fix $b,c$ in a way that it forms a non-degenerate triangle, then $m_a$ is unique). Could you confirm it?