I have been wondering if a shape/curve that has a line of symmetry along the lines $y=0$ and $y=-x$ is guaranteed to also have lines of symmetry along the lines $x=0$ and $y=x$.
My gut feeling tells me that this is true. All the shapes that I can think of satisfy this. But I can't think of a way to prove this.
Also, is this relationship "if and only if" (with a $\Leftrightarrow$ symbol) or just "implies" (with a $\Rightarrow$ symbol).
I tried looking up similar questions here but I couldn't find any. Maybe I worded it too verbosely.