Question

stepstatementreason1abcd is a squaregiven2∠abc≅∠bcdin a square, all angles are congruent3bc≅bcreflexive property4type of statement5△abc≅△dcbsas6∠bae≅∠cdecorresponding parts of congruent triangles are congruent (cpctc)

Explanation:

Step1: Analyze the properties of a square

In a square \(ABCD\), \(AB = BC=CD = DA\) (all sides of a square are equal).

Step2: Use the SAS (Side - Angle - Side) congruence criterion

We know that \(\angle ABC\cong\angle BCD\) (Step 2), \(\overline{BC}\cong\overline{BC}\) (Step 3 - reflexive property). For the SAS criterion, we need another pair of equal sides. Since \(AB = CD\) (sides of a square), the statement in Step 4 should be \(\overline{AB}\cong\overline{CD}\)

Answer:

\(\overline{AB}\cong\overline{CD}\)