Question

1. in the figure, △bat≅△cat. which statement is true by cpctc? ∠bta≅∠atc (overline{ca}congoverline{sb}) ∠sac≅∠sca (overline{ab}congoverline{ct})

Explanation:

Step1: Recall CPCTC

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

Step2: Analyze each option

• For $\angle BTA\cong\angle ATC$: $\angle BTA$ and $\angle ATC$ are corresponding angles in $\triangle BAT$ and $\triangle CAT$ respectively. Since $\triangle BAT\cong\triangle CAT$, by CPCTC, corresponding angles are congruent.
• For $\overline{CA}\cong\overline{SB}$: These are not corresponding parts of $\triangle BAT$ and $\triangle CAT$.
• For $\angle SAC\cong\angle SCA$: These angles are not part of the congruent - triangle pair $\triangle BAT$ and $\triangle CAT$.
• For $\overline{AB}\cong\overline{CT}$: These are not corresponding sides of $\triangle BAT$ and $\triangle CAT$.

Answer:

$\angle BTA\cong\angle ATC$