Question

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. \\(overline{ab} cong overline{bc} cong overline{cd} cong overline{da}\\) 4. ?
5. \\(\triangle bad cong \triangle abc\\) 5. sas
6. \\(overline{bd} cong overline{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:

A square has the property that all its sides are congruent. In the proof, since \(ABCD\) is a square (given), by the definition of a square, all its sides (\(\overline{AB}\), \(\overline{BC}\), \(\overline{CD}\), \(\overline{DA}\)) are congruent. The second option about right - angles measuring \(90^{\circ}\) is related to angles (not sides). The definition of a diagonal is about a line segment connecting non - adjacent vertices (not relevant to side congruence). The definition of perpendicular is about the relationship between two lines (forming a right angle) and not about side congruence.

Answer:

all sides of a square are congruent