# Proofs of parallel planes theorems

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• Aug 7th 2006, 08:07 AM
OReilly
Proofs of parallel planes theorems
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 $\beta' = \beta$.
• Aug 7th 2006, 08:12 AM
Quick
Congrats
Just want to say congrats for becoming a super-member.
• Aug 7th 2006, 08:21 AM
OReilly
Quote:

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...