Question

step\tstatement\treason
1\t\\( \triangle b d f \cong \triangle c e f \\)
\\( \overline { a d } \cong \overline { a e } \\)\tgiven
2\t\\( \overline { b d } \cong \overline { c e } \\)\tcorresponding parts of congruent triangles are con (cpctc)
3\t\\( \overline { a b } \cong \overline { a c } \\)\tsubstitution

Explanation:

Step1: Use congruent triangles property

Since \(\triangle BDF\cong\triangle CEF\), by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, we have \(BD = CE\).

Step2: Use substitution

We know that \(AD\cong AE\). Also, \(AB=AD + BD\) and \(AC = AE+CE\). Substituting \(BD\) with \(CE\) (from step 1) and \(AD\) with \(AE\) (given), we get \(AB\cong AC\).

Answer:

The proof is completed as shown above.