Galileo's discovery shows that, to an observer on Earth, Venus has phases just like Earth's moon. How did this observation provide support for the heliocentric model of the solar system?

Galileo's discovery shows that, to an observer on Earth, Venus has phases just like Earth's moon. This observation provide support for the heliocentric model of the solar system as follows:

Galileo noticed the Moon is not flat, but rocky and rugged-just like the Earth did. He used his telescope to observe the Venus phases. Galileo's findings confirmed his confidence in the concept of Copernicus that Earth and remaining planets revolve around the Sun, i. e. Heliocentrism. While most individuals in Galileo's days assumed that the Earth was the center of the universe and that the Sun and planets revolved around it, i. e. geocentrism. The idea of geocentric was generally preferred by the prominent and strong Catholic Church, and when Galileo started writing papers on his belief in a heliocentric with a valid explanation, he was called to Rome to face the inquisition's charges towards him. Thus in early 1616 he was accused of being a heretic, but later he cleared of charges of "heresy" with warning that he should not spread his belief. But he pursued his astronomy research, and was increasingly confident that all planets revolved around the Sun. Therefore he published a book in 1632 which explained that Copernicus' heliocentric theory was appropriate. Thus after this finally he was charged by "heresy" and sentenced to life imprisonment in 1633, but due to his poor health he lived imprisonment under house arrest and finally died on January 8, 1642.