Question

f is the midpoint of \\( \overline{eg} \\). complete the proof that \\( \triangle efh \cong \triangle gfi \\).

Explanation:

Step1: Recall the SSS (Side - Side - Side) congruence criterion

The SSS congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Identify the sides of the triangles

In \(\triangle EFH\) and \(\triangle GFI\), we have \(\overline{FH}\cong\overline{FI}\) (given), \(\overline{EI}\cong\overline{EH}\) (given), and \(\overline{EF}\cong\overline{FG}\) (definition of mid - point).

Step3: Apply the SSS criterion

Since \(EF = FG\), \(FH=FI\), and \(EI = EH\), by the SSS (Side - Side - Side) congruence criterion, \(\triangle EFH\cong\triangle GFI\).

Answer:

SSS (Side - Side - Side) congruence criterion.