Question

statements reasons

1. abcd is a square 1. given
2. ∠dab, ∠abc, ∠bcd, and ∠cda are right angles 2. definition of a square
3. ∠dab ≅ ∠abc ≅ ∠bcd ≅ ∠cda 3. right angles are congruent
4. ab ≅ bc ≅ cd ≅ da 4. ?
5. △bad ≅ △abc 5. sas
6. bd ≅ ac 6. cpctc

what is the missing reason in the proof?
all sides of a square are congruent
all right angles measure 90°
definition of diagonal
definition of perpendicular

Explanation:

In a square, by its definition, all four sides are of equal length. This property directly implies that the sides \(AB\), \(BC\), \(CD\), and \(DA\) are congruent. The other options: "all right angles measure \(90^{\circ}\)" is about angles (not sides), "definition of diagonal" is about a line segment connecting non - adjacent vertices (not side congruence), and "definition of perpendicular" is about the relationship between two lines (not side congruence).

Answer:

all sides of a square are congruent