Question

1. if ( \triangle deccong\triangle bec ), which is true by cpctc? ( overline{ae}congoverline{ed} ) ( angle ebccongangle edc ) ( angle acongangle c ) ( overline{ae}congoverline{ec} )

Explanation:

Step1: Recall CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

CPCTC states that if two triangles are congruent, then their corresponding sides and angles are congruent.

Step2: Analyze each option

• For $\overline{AE}\cong\overline{ED}$: There is no information from $\triangle DEC\cong\triangle BEC$ that would make these segments congruent.
• For $\angle EBC\cong\angle EDC$: Since $\triangle DEC\cong\triangle BEC$, by CPCTC, $\angle EBC$ (corresponds to $\angle EDC$ in the congruent triangles) are congruent.
• For $\angle A\cong\angle C$: There is no relation from $\triangle DEC\cong\triangle BEC$ to these angles.
• For $\overline{AE}\cong\overline{EC}$: There is no information from $\triangle DEC\cong\triangle BEC$ that would make these segments congruent.

Answer:

$\angle EBC\cong\angle EDC$