Question

$\overline{be} \cong \overline{be}$
reflexive property
$\overline{ac} \cong \overline{ac}$
reflexive property
$\overline{ba} \cong \overline{ba}$
reflexive property
$\overline{ab} \cong \overline{cd}$
corresponding parts of congruent triangles are congruent (cpctc)
$\angle a \cong \angle c$
corresponding parts of congruent triangles are congruent (cpctc)
$\angle b \cong \angle d$
corresponding parts of congruent triangles are congruent (cpctc)
$\overline{ce} \cong \overline{ce}$
reflexive property
$\overline{ae} \cong \overline{ae}$
reflexive property
$\angle eab \cong \angle eab$
reflexive property
$\overline{bd} \cong \overline{ea}$
× reflexive property

Explanation:

Step1: Recall Reflexive Property

The Reflexive Property of Congruence for segments states that a segment is congruent to itself, i.e., \(\overline{XY}\cong\overline{XY}\) for any segment \(\overline{XY}\).

Step2: Analyze \(\overline{BD}\cong\overline{EA}\)

Here, \(\overline{BD}\) and \(\overline{EA}\) are two different segments (they have different endpoints). The Reflexive Property does not apply to two distinct segments, so the original justification (Reflexive Property) is incorrect. To justify \(\overline{BD}\cong\overline{EA}\), we would need to use triangle congruence (e.g., if \(\triangle BDE\cong\triangle EAD\) or another pair of triangles, then CPCTC) or given congruency markings in the diagram (like tick marks indicating congruent segments), but the Reflexive Property is not valid here.

Answer:

The statement \(\overline{BD}\cong\overline{EA}\) cannot be justified by the Reflexive Property. The correct justification (if applicable) would depend on triangle congruence (e.g., CPCTC if triangles containing these segments are congruent) or given congruency markings, but the Reflexive Property applies to a segment being congruent to itself, not two different segments.