Question

1. given △bat≅△cat

which statement is true by cpctc?
∠tac≅∠bta
bt≅ta
ct≅at
∠bat≅∠cat

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: Identify corresponding parts

In $\triangle BAT$ and $\triangle CAT$, $\angle BAT$ and $\angle CAT$ are corresponding angles.

Step3: Analyze options

• $\angle TAC$ and $\angle BTA$ are not corresponding angles.
• $\overline{BT}$ and $\overline{TA}$ are not corresponding sides.
• $\overline{CT}$ and $\overline{AT}$ are not corresponding sides.
• $\angle BAT$ and $\angle CAT$ are corresponding angles, so by CPCTC, $\angle BAT\cong\angle CAT$.

Answer:

$\angle BAT\cong\angle CAT$