Question

1. if $\triangle dec\cong\triangle bec$, which is true by cpctc?

$\angle bec\cong\angle dce$
$\angle bca\cong\angle bcd$
$\overline{be}\cong\overline{ed}$
$\overline{ac}\cong\overline{bd}$

Explanation:

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

If \(\triangle DEC\cong\triangle BEC\), then their corresponding parts are congruent.

Step2: Analyze each option

• For \(\angle BEC\cong\angle DCE\): These are not corresponding angles of \(\triangle DEC\) and \(\triangle BEC\).
• For \(\angle BCA\cong\angle BCD\): These angles are not part of the congruent triangles \(\triangle DEC\) and \(\triangle BEC\).
• For \(\overline{BE}\cong\overline{ED}\): In \(\triangle DEC\) and \(\triangle BEC\), \(BE\) and \(ED\) are corresponding sides. Since \(\triangle DEC\cong\triangle BEC\), by CPCTC, \(\overline{BE}\cong\overline{ED}\).
• For \(\overline{AC}\cong\overline{BD}\): These segments are not part of the congruent triangles \(\triangle DEC\) and \(\triangle BEC\).

Answer:

\(\overline{BE}\cong\overline{ED}\)