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Math Help - 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 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 .
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    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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