Proofs of parallel planes theorems

**OReilly** · August 7th 2006, 08:07 AM

Can someone check are my proofs correct?

Theorem 1: If there are two intersecting lines $p$ and $q$ which are parallel to plane $\alpha$ , then lines $p$ and $q$ determines plane $\beta$ which is parallel to plane $\alpha$ .

Proof: Lines $p$ and $q$ determines plane $\beta$ which doesn't have common points with $\alpha$ so if $\alpha \cap \beta = \emptyset$ then planes $\alpha$ and $\beta$ are parallel.

Theorem 2: Through given point $B$ there is only one plane that is parallel to given plane $\alpha$ .

Proof: Lets say that plane $\beta$ goes through point $B$ which is parallel to plane $\alpha$ . If there is another plane for example $\beta'$ that would go through point $B$ which is parallel to plane $\alpha$ then it would be $\beta' = \beta$ .

**Quick** · August 7th 2006, 08:12 AM

Just want to say congrats for becoming a super-member.

**OReilly** · August 7th 2006, 08:21 AM

Originally Posted by Quick

Just want to say congrats for becoming a super-member.

Thanks! I really didn't notice! But I am far far away from being super math member... But I love it and learn it...

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