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Justify triangle congruence


Below are ABC and DEF. We assume that AB=DE, BC=EF, and mB=mE.
Here is a rough outline of a proof that ABCDEF:
  1. We can map ABC using a sequence of rigid transformations so that A=D and B=E.
  2. If C and F are on the same side of DE, then C=F.
  3. If C and F are on opposite sides of DE, then we reflect ABC across DE and then C=F, A=D and B=E.
What is the justification that C=F in step 2?
Choose 1 answer: