Find the minimum index of refraction of prism for a beam to be totally internally reflected 4 56

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Optics 4th/5th Edition Problem 4-56
Eugene Hecht
A prism, ABC, is configured such that angle BCA = 90° and angle CBA = 45°. What is the minimum value of its index of refraction if, while immersed in air, a beam traversing face AC is to be totally internally reflected from face BC?
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How do you know for certain that the angle of incidence is 45 degrees? I understand the rest, but why must the incident beam (inside the prism) bend (from the original incident angle) at the same angle as the prism does, aka CBA?

mrguy