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Math Help - Proof of congruent triangle construction

  1. #1
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    Proof of congruent triangle construction

    Theorem: Given triangle ABC, segment DE such that DE = AB, and H is a half-plane bounded by the line DE, then there is a unique point F that is an element of H such that triangle DEF is congruent to triangle ABC.

    What I have so far:
    Givens stated above. By the protractor postulate, there exists a unique ray -DG-> such that G is in H and <BAC = <EDG. By the ruler postulate, there must be a point F on -DG-> such that DF=AC. Thus by Side-Angle-Side, triangles ABC and DEF are congruent.

    How do I go about proving the uniqueness of F though??
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  2. #2
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    Quote Originally Posted by spectralsea View Post
    Theorem: Given triangle ABC, segment DE such that DE = AB, and H is a half-plane bounded by the line DE, then there is a unique point F that is an element of H such that triangle DEF is congruent to triangle ABC.

    What I have so far:
    Givens stated above. By the protractor postulate, there exists a unique ray -DG-> such that G is in H and <BAC = <EDG. By the ruler postulate, there must be a point F on -DG-> such that DF=AC. Thus by Side-Angle-Side, triangles ABC and DEF are congruent.

    How do I go about proving the uniqueness of F though??
    What are the exact words of the "ruler postulate"? Doesn't it include the uniqueness, as well as the existence, of the point?
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