Sun and Moon

The Sun and Moon, in relation to Earth, display some very remarkable and "coincidental" commonalities.

Sun and Moon rotate at the same velocity

Yes, it's true.  In addition to the Moon spinning at the same rate of rotation around the Earth (27 days), the Sun's average rotational velocity is also 27 days.

Sun and Moon appear to us as the same diameter

From Astronomy.com:

Why is the Moon exactly the same apparent size from Earth as the Sun? Surely this cannot be just coincidence; the odds against such a perfect match are enormous.