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Math Help - Help with a proof dealing with isometries

  1. #1
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    Help with a proof dealing with isometries

    Hey I need some help on how to prove something:
    Suppose f is an isometry. Prove triangle ABC is congruent to triangle f(A) f(B) f(C).

    I think I have to start by stating the coordinates for example triangle ABC has points A=(x1,y1) b=(x2,y2)... But I am not sure I think that f(A) = (x'1,y'1). If anyone knows anything that would help me I would appreciate it.
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  2. #2
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    Since f is an isometry, by definition it must preserve distance. Therefore, AB=f(A) f(B), AC=f(A) f(C) and BC=f(B) f(C). Now, since the three sides of ABC are equal to the 3 sides of f(A)f(B)f(C), the 2 triangles must be congruent.
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  3. #3
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    Thanks for your help. That makes sense.
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