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Thread: Proofs of parallel planes theorems

  1. #1
    Senior Member OReilly's Avatar
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    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 $.
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  2. #2
    MHF Contributor Quick's Avatar
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    Congrats

    Just want to say congrats for becoming a super-member.
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  3. #3
    Senior Member OReilly's Avatar
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    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...
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