Question

A square with vertices upper S, upper D, upper G, and upper F (in that order). There are two dashed diagonals that intersect at point upper L.
Identify the two statements that would guarantee SDGF is a square.

(1 point)
Responses

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

SD¯¯¯¯¯¯¯⊥FG¯¯¯¯¯¯¯¯
line segment cap s cap d perpendicular to line segment cap f cap g

SG¯¯¯¯¯¯¯∥DF¯¯¯¯¯¯¯¯
line segment cap s cap g is parallel to line segment cap d cap f

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

SF¯¯¯¯¯¯¯⊥FG¯¯¯¯¯¯¯¯

Answer 1

To guarantee that quadrilateral SDGF is a square, you would need to confirm both the lengths of the sides and the angles between adjacent sides. The following two statements would be sufficient:

1. **SF ¯¯¯¯¯¯¯ ≅ FG ¯¯¯¯¯¯¯¯**: This ensures that the length of side SF is equal to the length of side FG, which is a necessary condition for being a square.

2. **SF ¯¯¯¯¯¯¯ ⊥ FG ¯¯¯¯¯¯¯¯**: This ensures that the sides SF and FG are perpendicular to each other, confirming a right angle that is also necessary for the shape to be a square.

Thus, the two statements that would guarantee SDGF is a square are:

1. \( SF \cong FG \)
2. \( SF \perp FG \)