Theta-Ratio of a Simplex Method for a degenerate solution, are they always equal?

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Are the $\theta$-ratios of two degenerate solutions always equal?

So as to say:

If we know two unique points yield the same objective value, must their $\theta$-ratios always be equal?

For two different bases $x_1$, $x_2$, with $x_1\neq x_2$.

(Something I've been thinking about)