To guarantee that a quadrilateral \( SDGF \) is a square, we need to confirm that it has both equal sides and right angles. The statements that would help meet these criteria are:
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\( \overline{DG} \cong \overline{DF} \): This states that the segments \( DG \) and \( DF \) are congruent, which indicates that two sides of the quadrilateral are of equal length.
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\( \overline{SF} \perp \overline{FG} \): This states that the segment \( SF \) is perpendicular to segment \( FG \), ensuring that there is a right angle between these two sides.
Thus, the combination of equal side lengths and right angles will ensure that the quadrilateral is indeed a square.
In conclusion, the statements you need are:
- \( \overline{DG} \cong \overline{DF} \)
- \( \overline{SF} \perp \overline{FG} \)
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