Question

Identify the two statements that would guarantee SDGF
𝑆
𝐷
𝐺
𝐹
is a square.

(1 point)
Responses

DG¯¯¯¯¯¯¯¯≅DF¯¯¯¯¯¯¯¯
𝐷
𝐺
¯
≅
𝐷
𝐹
¯
line segment cap d cap g is congruent to line segment cap d cap f

SF¯¯¯¯¯¯¯≅FG¯¯¯¯¯¯¯¯
𝑆
𝐹
¯
≅
𝐹
𝐺
¯
line segment cap s cap f is congruent to line segment cap f cap g

SF¯¯¯¯¯¯¯⊥FG¯¯¯¯¯¯¯¯
𝑆
𝐹
¯
⊥
𝐹
𝐺
¯
line segment cap s cap f perpendicular to line segment cap f cap g

SG¯¯¯¯¯¯¯∥DF¯¯¯¯¯¯¯¯
𝑆
𝐺
¯
∥
𝐷
𝐹
¯
line segment cap s cap g is parallel to line segment cap d cap f

SD¯¯¯¯¯¯¯⊥FG¯¯¯¯¯¯¯¯

Answer 1

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:

1. **\( \overline{DG} \cong \overline{DF} \)**: This states that the segments \( DG \) and \( DF \) are congruent, which indicates that two sides of the quadrilateral are of equal length.

2. **\( \overline{SF} \perp \overline{FG} \)**: 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:
- \( \overline{DG} \cong \overline{DF} \)
- \( \overline{SF} \perp \overline{FG} \)