Question

1. abcd is a square
2. ∠dab, ∠abc, ∠bcd, and ∠cda are right angles
3. ∠dab ≅ ∠abc ≅ ∠bcd ≅ ∠cda
4. \overline{ab} ≅ \overline{bc} ≅ \overline{cd} ≅ \overline{da}
5. △bad ≅ △abc
6. \overline{bd} ≅ \overline{ac}

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 very definition, all four sides are of equal length. This property is fundamental to the geometric structure of a square. When we say \( \overline{AB}\cong\overline{BC}\cong\overline{CD}\cong\overline{DA}\), it is because of the characteristic that all sides of a square are congruent. The other options:

• "All right angles measure \(90^{\circ}\)" is related to the angle - measure property of a square, not the side - congruence.
• "Definition of diagonal" is about the line segment connecting non - adjacent vertices, which is not relevant here.
• "Definition of perpendicular" is about the relationship between two lines (forming a \(90^{\circ}\) angle), not about side congruence.

Answer:

all sides of a square are congruent