The mistake in Fox's proof is found in Reason 5. The reasoning states that "△ABD≅△ACD" is proven by the "SAS Congruence Theorem," but the correct application here is actually based on the "SSS Congruence Theorem."
To fix this mistake, the statement should correctly indicate that the triangles are congruent by the SSS Congruence Theorem because:
- AB and AC are congruent (given),
- AD is common to both triangles (from the reflexive property),
- BD and CD are congruent since D is the midpoint of BC.
Thus, the correct reasoning in Step 5 should read:
"5. △ABD≅△ACD by SSS Congruence Theorem."
The other statements and reasons in Fox's proof appear to be correct given the isosceles triangle conditions and the construction of the midpoint and angle bisector.