As far as I can tell, not being an astronomer, the only way to measure the distance of a star using geometry is by measuring stellar parallax and angular diameter. The problem with angular diameter is that not all stars are the same diameter. A more distant, larger star could have the same angular diameter as a closer, smaller star and so it becomes more difficult to determine which star is closer. That’s when astronomers begin measuring things with a spectrophotometer and other instruments. Astronomers say that even the closest stars are light-years away.
If you believe that the earth is round and that it orbits the sun along with the other planets in our solar system, then you must conclude that the stars are at least as far away as the farthest planet. Thanks to Johannes Kepler and others we have a pretty good idea how far away the planets are.