Question

1. if ( \triangle abccong\triangle adc ), which is not true by cpctc? ( overline{be}congoverline{de} ) ( overline{ab}congoverline{ad} ) ( angle baccongangle dac ) ( angle bcacongangle dce )

Explanation:

Step1: Understand CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) states that if two triangles are congruent, then their corresponding sides and angles are congruent.

Step2: Analyze each option

• For $\overline{AB}\cong\overline{AD}$: Since $\triangle ABC\cong\triangle ADC$, $AB$ and $AD$ are corresponding sides. So, $\overline{AB}\cong\overline{AD}$ by CPCTC.
• For $\angle BAC\cong\angle DAC$: $\angle BAC$ and $\angle DAC$ are corresponding angles of $\triangle ABC$ and $\triangle ADC$. So, $\angle BAC\cong\angle DAC$ by CPCTC.
• For $\angle BCA\cong\angle DCA$ (assuming it's a typo for $\angle DCE$ in the context of the triangles): $\angle BCA$ and $\angle DCA$ (or $\angle DCE$ if it's a mis - label) are corresponding angles of $\triangle ABC$ and $\triangle ADC$. So, $\angle BCA\cong\angle DCA$ (or relevant angle) by CPCTC.
• For $\overline{BE}\cong\overline{DE}$: $BE$ and $DE$ are not sides of $\triangle ABC$ and $\triangle ADC$. They are parts of other sub - triangles ($\triangle ABE$ and $\triangle ADE$). So, $\overline{BE}\cong\overline{DE}$ is not a result of CPCTC for $\triangle ABC\cong\triangle ADC$.

Answer:

$\overline{BE}\cong\overline{DE}$