NavList:

I think the statement that rays are parallel is different from parallelism in the context of parallax. In the former, we are interested in the angle between two rays from the source, which strike either side of whatever aperture we're using to observe the object- our eye pupil, the diameter of our binocs or sextant telescope. This is vanishingly small, as we say in mathematics! However, as you say, if the base angle is not the eye pupil but the 2x92 million miles of the Earth's position 6 months apart, it is NOT vanishingly small anymore, but when we design the imaging optics in a telescope we are unconcerned with this angle. This parallax angle defines the angular difference of the bearing of a star, or, said another way, it's relative position with respect with objects much farther away.

The idea of non-parallelism is used to define a unit of stellar distance, the parsec. An object which, when viewed 6 months apart, appears to have changed it's bearing by 1 second, is at a distance, by definition, of exactly 1 parsec (an incredible distance 3.2 Light years, trillions of miles.

It's a silly unit of measure, if you ask me, because the nearer an object to us, the BIGGER the parallax, yet it comes up measuring a smaller number for the distance measured in parsecs. Actually, the change in angle, in parsecs due to parallex is the inverse of the distance in parsecs.

http://lcogt.net/spacebook/parallax-and-distance-measurement

Above, a link to a nice description of distance by parallax and the limitations.

By the way, this idea of parallel rays from a distant object is the hardest thing for Optics students to grasp, at first. I think it's because one can not see the apex of the fan of rays (off scale, as we say).

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