Question

1. in the figure, △bat≅△cat. which statement is not true by cpctc?

ta = at
∠cas≅∠bas
∠cab≅∠sab
tb = tc

Explanation:

Step1: Recall CPCTC concept

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

Step2: Analyze each option

• $\overline{TA}=\overline{AT}$ is always true as it's the same segment (reflexive property), but not a result of CPCTC for $\triangle BAT$ and $\triangle CAT$.
• $\angle CAS\cong\angle BAS$: Since $\triangle BAT\cong\triangle CAT$, $\angle BAT\cong\angle CAT$. And if we consider the angle - bisector property (implied by the congruence of the large triangles), $\angle CAS\cong\angle BAS$ by CPCTC.
• $\angle CAB$ and $\angle SAB$ are not corresponding angles of $\triangle BAT$ and $\triangle CAT$. $\angle CAB$ is not related to $\angle SAB$ in terms of the congruence of $\triangle BAT$ and $\triangle CAT$ by CPCTC.
• $\overline{TB}\cong\overline{TC}$ because they are corresponding sides of congruent triangles $\triangle BAT$ and $\triangle CAT$ (by CPCTC).

Answer:

C. $\angle CAB\cong\angle SAB$