Question

1. in the figure, \\( \triangle bat\cong\triangle cat \\). which statement is not true by cpctc?

\\( \overline { s b } \cong \overline { s t } \\)
\\( \angle b a t \cong \angle c a t \\)
\\( \angle b t a \cong \angle c t a \\)
\\( \overline { a b } \cong \overline { a c } \\)

Explanation:

Step1: Recall the definition of CPCTC

CPCTC (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 \(\angle BAT\) and \(\angle CAT\): These are corresponding angles of \(\triangle BAT\) and \(\triangle CAT\). By CPCTC, \(\angle BAT\cong\angle CAT\).
• For \(\angle BTA\) and \(\angle CTA\): These are corresponding angles of \(\triangle BAT\) and \(\triangle CAT\). By CPCTC, \(\angle BTA\cong\angle CTA\).
• For \(\overline{AB}\) and \(\overline{AC}\): These are corresponding sides of \(\triangle BAT\) and \(\triangle CAT\). By CPCTC, \(\overline{AB}\cong\overline{AC}\).
• For \(\overline{SB}\) and \(\overline{ST}\): There is no information from \(\triangle BAT\cong\triangle CAT\) that directly gives \(\overline{SB}\cong\overline{ST}\) by CPCTC.

Answer:

\(\overline{SB}\cong\overline{ST}\)