Can someone check are my proofs correct?
Theorem 1: If there are two intersecting lines and which are parallel to plane , then lines and determines plane which is parallel to plane .
Proof: Lines and determines plane which doesn't have common points with so if then planes and are parallel.
Theorem 2: Through given point there is only one plane that is parallel to given plane .
Proof: Lets say that plane goes through point which is parallel to plane . If there is another plane for example that would go through point which is parallel to plane then it would be .