the evidence that the earth and the moon were formed at the same time?

Answer 1

There's strong evidence that the Earth was formed first, and that the moon was created later by something large striking the earth and knocking a lump out of it which formed into the moon. The composition of the moon is the same as that of the Earth's mantle, which suggests that it formed from the Earth's mantle after the Earth had separated into the differerent layers that it currently has.

Answer 2

They were not. The current theory of the Moon's formation is that it was created by the collision of a Mars-sized body with the Earth, about a billion years after the Earth itself formed.

Answer 3

The moon is held in perfect sync with the earth by a gravity gradient. It is that the side near earth has more mass than the other half.