As ProfRob pointed out, Venus is never in opposition to the Sun. This means it’s never 180° from the Sun. Moreover, it’s never more than about 47° from the Sun. That, by itself, is a first hint, but let’s say, for the sake of argument, that we still think it somehow turns around the Earth (on an epicycle [small circle] that turns on a deferent [larger circle], in Ptolemy’s model).
So, we have established that Venus is never far from the Sun in Earth’s sky. Don’t do the following experiment with the Sun, but a lamp whose light is bearable to your eyes will suffice. Place your finger between your face and the lamp. Do you see your finger as fully lit? No. You always see at least part of it that’s shaded, just like Venus in your second image.
But now, if you allow your finger to go past the lamp, then you can see it fully lit.
Technically, it doesn’t prove that Venus revolves around the Sun per se, as its epicycle could simply be large enough to encompass the Sun. However, Mercury shows the same phases (sometimes fully lit when it’s on the other side of the Sun, but sometimes a thin crescent when it’s closer to the Earth). Now, it would be quite a coincidence that both planets would have epicycles that encompass the Sun, wouldn’t it?
Another very important clue, as ProfRob mentioned, is the angular size of the planet’s disk and how it changes with time. Simple geometry can be used to demonstrate that the epicycle would not only encompass the Sun, but actually be centered on it.
The final nail in the coffin of geocentrism, though, was the discovery of the galilean satellites around Jupiter. It proved that celestial objects could revolve around other things than the Earth—in occurrence, around the planet Jupiter. Then we discovered satellites to Saturn, etc.
Before I conclude, I’d like to point out that the “Copernican Revolution” would better be named the “Keplerian Revolution,” as Copernicus’s model was very slowly accepted by scientists, as it did not offer anything better than Ptolemy’s model—actually, it’s almost the exact same as Ptolemy’s model, but “shifted” to a solar point of view. There were even two epicycles for the Moon, where Ptolemy had only one. And while instruments were not precise enough to reveal the difference at the time Copernicus’s De Revolutionibus was published, Tycho Brahe soon discovered instrumental and personal errors and took steps to compensate for them, allowing much better measurements. Kepler eventually complained that Copernicus’s model was five degrees off compared to actual observations—that’s a huge difference, the size of about three fingers held at arm’s length!
When in 1609 Kepler discovered that planetary orbits are (to first approximation) ellipses, then theory was found to perfectly fit with observations. The same year, Galileo discovered Jupiter’s four largest moons, and geocentrism was buried once and for all.
