Question

state what additional information is required to prove \\( \triangle y g e \cong \triangle f g e \\) by sss.

Explanation:

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

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

Step2: Identify the given sides

From the figure, we know that \(FY\) has two segments \(FY = FG+GY\) (but not directly relevant here). We are given that \(YE = FE\) (marked with one tick) and \(GE\) is common to both \(\triangle YGE\) and \(\triangle FGE\).

Step3: Determine the missing side

For \(\triangle YGE\cong\triangle FGE\) by SSS, we need \(YG = FG\)

Answer:

The additional information required is \(YG = FG\)