Question

1. in the diagram, △abc≅△edc. which statement is not necessarily true?

de≅ab
∠b≅∠d
bc≅ce
∠a≅∠e

Explanation:

Step1: Recall congruent - triangle properties

If $\triangle ABC\cong\triangle EDC$, then corresponding sides and corresponding angles are equal.
Corresponding sides: $\overline{AB}\cong\overline{ED}$, $\overline{BC}\cong\overline{DC}$, $\overline{AC}\cong\overline{EC}$.
Corresponding angles: $\angle A\cong\angle E$, $\angle B\cong\angle D$, $\angle ACB\cong\angle ECD$.

Step2: Analyze each option

• Option 1: $\overline{DE}\cong\overline{AB}$ is True because they are corresponding sides of congruent triangles $\triangle ABC$ and $\triangle EDC$.
• Option 2: $\angle B\cong\angle D$ is True because they are corresponding angles of congruent triangles $\triangle ABC$ and $\triangle EDC$.
• Option 3: $\overline{BC}\cong\overline{CE}$ is Not True. The correct corresponding - side pair is $\overline{BC}\cong\overline{DC}$ and $\overline{AC}\cong\overline{EC}$.
• Option 4: $\angle A\cong\angle E$ is True because they are corresponding angles of congruent triangles $\triangle ABC$ and $\triangle EDC$.

Answer:

$\overline{BC}\cong\overline{CE}$