Question

1. in the figure, △bat≅△cat. which statement is not true by cpctc? ∠bta≅∠cta (overline{ab}congoverline{ac}) ∠bat≅∠cat (overline{sb}=overline{st})

Explanation:

Step1: Recall CPCTC

CPCTC stands for Corresponding - Parts of Congruent Triangles are Congruent. If $\triangle BAT\cong\triangle CAT$, then corresponding angles and corresponding sides are congruent.

Step2: Analyze each option

• For $\angle BTA\cong\angle CTA$, $\angle BTA$ and $\angle CTA$ are corresponding angles of $\triangle BAT$ and $\triangle CAT$, so this is true by CPCTC.
• For $\overline{AB}\cong\overline{AC}$, $\overline{AB}$ and $\overline{AC}$ are corresponding sides of $\triangle BAT$ and $\triangle CAT$, so this is true by CPCTC.
• For $\angle BAT\cong\angle CAT$, $\angle BAT$ and $\angle CAT$ are corresponding angles of $\triangle BAT$ and $\triangle CAT$, so this is true by CPCTC.
• For $\overline{SB}\cong\overline{ST}$, $S$ is the intersection of the diagonals of the figure formed by the two congruent triangles. There is no information from $\triangle BAT\cong\triangle CAT$ that makes $\overline{SB}$ and $\overline{ST}$ corresponding parts. So this is not true by CPCTC.

Answer:

$\overline{SB}\cong\overline{ST}$