Question

select the statement that guarantee $overline{ef}$ is congruent to $overline{gh}$. draw show your work here $\triangle efgcong\triangle fgh$ by the side - side - side criterion $overline{eg}paralleloverline{fh}$ $ef = gh$ $eg = fh$ $\triangle eghcong\triangle fgh$ by the side - side - side criterion

Explanation:

Step1: Recall congruent - segment definition

Two segments are congruent if and only if they have the same length.

Step2: Analyze each option

• For $\triangle EFG\cong\triangle FGH$ by SSS, we cannot directly get $EF\cong GH$ from this congruence of triangles.
• $\overline{EG}\parallel\overline{FH}$ gives information about parallel - lines, not about the congruence of $EF$ and $GH$.
• If $EF = GH$, by the definition of congruent segments (segments with equal lengths are congruent), $\overline{EF}\cong\overline{GH}$.
• $EG = FH$ does not guarantee $EF\cong GH$.
• $\triangle EGH\cong\triangle FGH$ by SSS is not a valid congruence (as they share side $GH$ and the other two - side equalities are not given to satisfy SSS for these two triangles), and also it does not directly imply $EF\cong GH$.

Answer:

$EF = GH$