Question

in the diagram below, △aec≅△bed. which statement is not always true?

• $overline{ce}congoverline{de}$
• $angle acecongangle dbe$
• $angle eaccongangle ebd$
• $overline{ac}congoverline{bd}$

Explanation:

Step1: Recall congruent - triangle properties

If $\triangle AEC\cong\triangle BED$, then corresponding sides and corresponding angles are congruent.
Corresponding sides: $\overline{AC}\cong\overline{BD}$, $\overline{AE}\cong\overline{BE}$, $\overline{CE}\cong\overline{DE}$.
Corresponding angles: $\angle EAC\cong\angle EBD$, $\angle ACE\cong\angle BDE$, $\angle AEC\cong\angle BED$.

Step2: Analyze each option

• Option 1: $\overline{CE}\cong\overline{DE}$ is a corresponding - side relationship for $\triangle AEC\cong\triangle BED$, so it is always true.
• Option 2: $\angle ACE\cong\angle DBE$ is incorrect. The correct congruent - angle pair is $\angle ACE\cong\angle BDE$ and $\angle ACE

ot\cong\angle DBE$ in general.

• Option 3: $\angle EAC\cong\angle EBD$ is a corresponding - angle relationship for $\triangle AEC\cong\triangle BED$, so it is always true.
• Option 4: $\overline{AC}\cong\overline{BD}$ is a corresponding - side relationship for $\triangle AEC\cong\triangle BED$, so it is always true.

Answer:

$\angle ACE\cong\angle DBE$