# Proofs of parallel planes theorems

• 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 $\displaystyle p$ and $\displaystyle q$ which are parallel to plane $\displaystyle \alpha$, then lines $\displaystyle p$ and $\displaystyle q$ determines plane $\displaystyle \beta$ which is parallel to plane $\displaystyle \alpha$.

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

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

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