Identify the statements that would need to be true for ASDF

Question

𝐴
𝑆
𝐷
𝐹
to be a square.

(1 point)
Responses

∠DFW=90∘
∠
𝐷
𝐹
𝑊
=
90
∘
angle cap d cap f cap w is equal to 90 degrees

∠SDF=90∘
∠
𝑆
𝐷
𝐹
=
90
∘
angle cap s cap d cap f is equal to 90 degrees

∠SAF=45∘
∠
𝑆
𝐴
𝐹
=
45
∘
angle cap s cap A cap f is equal to 45 degrees

∠FWA=90∘
∠
𝐹
𝑊
𝐴
=
90
∘
angle cap f cap w cap A is equal to 90 degrees

∠AWF=45∘

Answer 1

For quadrilateral ASDF to be classified as a square, the following conditions must be true:

1. All sides must be equal in length.
2. All angles must be right angles (90 degrees).
3. The diagonals must be equal in length and bisect each other at right angles.

Given the statements you provided, the following need to be true for ASDF to be a square:

1. ∠DFW = 90° - This indicates there is a right angle at vertex D, which is necessary for the shape to have right angles.
2. ∠SDF = 90° - This indicates there is a right angle at vertex S, which is necessary for the shape to have right angles.
3. ∠FWA = 90° - This indicates there is a right angle at vertex F, which is necessary for the shape to have right angles.

The statement ∠SAF = 45° does not need to be true for ASDF to be a square, as all angles in a square are 90 degrees.

The statement ∠AWF = 45° also does not need to be true because it is not required for a square to have any angles of 45 degrees.

In conclusion, the statements that need to be true for ASDF to be a square are:

1. ∠DFW = 90°
2. ∠SDF = 90°
3. ∠FWA = 90°