The additional information that we need to know before we can prove that [tex]\triangle EFG\cong \triangle YXW[/tex] by the SSS Congruence Theorem is: D) GE ≅ WY
Recall:
The Side-Side-Side Congruence Theorem (SSS) states that two triangles can be defined as congruent to each other, if the corresponding three sides of both triangles are congruent to each other.
In the image given,
[tex]EF \cong YX\\\\GF \cong WX[/tex]
This means two corresponding angles of [tex]\triangle EFG $ and $ \triangle YXW[/tex] are congruent to each other.
We cannot conclude that both triangles are congruent except we know for sure that the third sides, GE and WY are congruent to each other.
Therefore, the additional information that we need to know before we can prove that [tex]\triangle EFG\cong \triangle YXW[/tex] by the SSS Congruence Theorem is: D) GE ≅ WY
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