Question

1. in the diagram, $\triangle abccong\triangle edc$. which statement is not necessarily true? $overline{de}congoverline{ab}$ $angle acongangle e$ $angle bcongangle d$ $overline{bc}congoverline{ce}$

Explanation:

Step1: Recall the properties of congruent triangles

If \(\triangle ABC\cong\triangle EDC\), then corresponding parts are congruent. That is, \(\overline{AB}\cong\overline{ED}\), \(\angle A\cong\angle E\), \(\angle B\cong\angle D\), \(\overline{BC}\cong\overline{DC}\), \(\overline{AC}\cong\overline{EC}\)

Step2: Analyze each option

• For \(\overline{DE}\cong\overline{AB}\): Since \(\triangle ABC\cong\triangle EDC\), by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \(\overline{DE}\cong\overline{AB}\)
• For \(\angle A\cong\angle E\): By CPCTC, \(\angle A\cong\angle E\)
• For \(\angle B\cong\angle D\): By CPCTC, \(\angle B\cong\angle D\)
• For \(\overline{BC}\cong\overline{CE}\): From \(\triangle ABC\cong\triangle EDC\), we have \(\overline{BC}\cong\overline{DC}\), not necessarily \(\overline{BC}\cong\overline{CE}\)

Answer:

\(\overline{BC}\cong\overline{CE}\) (the fourth option)