Question

what else would need to be congruent to show that △ efg ≅ △ hij by sss? given: \\(\overline{ef} \cong \overline{hi}\\) \\(\overline{fg} \cong \overline{ij}\\) a. \\(\overline{eg} \cong \overline{hj}\\) b. \\(\overline{fg} \cong \overline{hi}\\) c. \\(\angle f \cong \angle i\\) d. \\(\overline{ef} \cong \overline{hj}\\)

Explanation:

To show \(\triangle EFG \cong \triangle HIJ\) by SSS (Side - Side - Side) congruence criterion, we need all three corresponding sides of the triangles to be congruent. We are already given that \(\overline{EF}\cong\overline{HI}\) and \(\overline{FG}\cong\overline{IJ}\). The third pair of corresponding sides should be \(\overline{EG}\) (from \(\triangle EFG\)) and \(\overline{HJ}\) (from \(\triangle HIJ\)). So, we need \(\overline{EG}\cong\overline{HJ}\) to satisfy the SSS criterion. Option B is incorrect as \(\overline{FG}\) and \(\overline{HI}\) are not corresponding sides. Option C is about angles, and SSS is a side - based criterion. Option D has non - corresponding sides.

Answer:

A. \(\overline{EG}\cong\overline{HJ}\)