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Math Help - Image/preimage transformation

  1. #1
    Senior Member sfspitfire23's Avatar
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    Image/preimage transformation

    Prove If \alpha \cong \beta and T(\alpha)=\alpha ', T(\beta)=\beta ' where T is an isometry, then \alpha ' \cong \beta '

    I think I need to start with alpha prime and get to alpha....but im not sure how to show this...
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by sfspitfire23 View Post
    Prove If \alpha \cong \beta and T(\alpha)=\alpha ', T(\beta)=\beta ' where T is an isometry, then \alpha ' \cong \beta '

    I think I need to start with alpha prime and get to alpha....but im not sure how to show this...
    There is no context here. What are \alpha,\beta? Is this an isometry between metric spaces or one in just geometry?
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  3. #3
    Senior Member sfspitfire23's Avatar
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    sorry, just geometry
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by sfspitfire23 View Post
    sorry, just geometry
    Ok. So what are \alpha,\beta?
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  5. #5
    Senior Member sfspitfire23's Avatar
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    Ah, they are point sets
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by sfspitfire23 View Post
    Ah, they are point sets
    and lastly...what does it mean for two point sets to be congruent?
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  7. #7
    Senior Member sfspitfire23's Avatar
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    two sets where one is the image of the other over a transformation...
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  8. #8
    Senior Member sfspitfire23's Avatar
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    Hm, then it would seem i could do this proof by definition almost i believe
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