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**spectralsea** 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??