Final answer:
The statement is true; the more distant a star is, the smaller its parallax angle becomes, as the apparent movement is less when viewed from Earth.
Step-by-step explanation:
The statement 'The more distant a star, the smaller its parallax' is true. Stellar parallax is the apparent shift in position of a star when viewed from two different positions, specifically from opposite ends of Earth's orbit around the Sun. As a star's distance from Earth increases, its parallax angle decreases because the star's apparent movement is smaller relative to the background stars. This phenomenon is similar to noticing how nearby objects move more in relation to your line of sight when you move, compared to objects that are far away which seem to hardly move at all.
To further illustrate, a star with a parallax of 0.1 arcsecond is calculated to be 10 parsecs away from Earth, while one with a parallax of 0.05 arcsecond is 20 parsecs away. This mathematical relationship clearly indicates that the star twice as far away has half the parallax, thus confirming the initial claim is true.