Question

1. if △abc≅△adc, which is not true by cpctc?

be≅de
ab≅ad
∠bca≅∠dce
∠bac≅∠dac

Explanation:

Step1: Recall CPCTC concept

CPCTC (Corresponding - Parts of Congruent Triangles are Congruent). If \(\triangle ABC\cong\triangle ADC\), then corresponding sides and corresponding angles are congruent.

Step2: Analyze each option

• For \(\overline{AB}\) and \(\overline{AD}\), they are corresponding sides of \(\triangle ABC\) and \(\triangle ADC\), so \(\overline{AB}\cong\overline{AD}\) by CPCTC.
• For \(\angle BCA\) and \(\angle DCA\), they are corresponding angles of \(\triangle ABC\) and \(\triangle ADC\), so \(\angle BCA\cong\angle DCA\) by CPCTC.
• For \(\angle BAC\) and \(\angle DAC\), they are corresponding angles of \(\triangle ABC\) and \(\triangle ADC\), so \(\angle BAC\cong\angle DAC\) by CPCTC.
• There is no information from \(\triangle ABC\cong\triangle ADC\) that directly gives \(\overline{BE}\cong\overline{DE}\) by CPCTC.

Answer:

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