Question

1. given: \\( \triangle bat \cong \triangle cat \\) which statement is not true by cpctc? \\( \overline{ab} \cong \overline{ac} \\) \\( \angle bat \cong \angle cat \\) \\( \angle bta \cong \angle cta \\) \\( \overline{ab} \cong \overline{ct} \\)

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: Identify corresponding parts

• For \(\triangle BAT\) and \(\triangle CAT\):
• Corresponding sides: \(\overline{AB}\) corresponds to \(\overline{AC}\), \(\overline{BT}\) corresponds to \(\overline{CT}\), \(\overline{AT}\) corresponds to \(\overline{AT}\) (common side).
• Corresponding angles: \(\angle BAT\) corresponds to \(\angle CAT\), \(\angle BTA\) corresponds to \(\angle CTA\), \(\angle ABT\) corresponds to \(\angle ACT\).

Step3: Analyze each option

• \(\overline{AB}\cong\overline{AC}\): True, as they are corresponding sides.
• \(\angle BAT\cong\angle CAT\): True, as they are corresponding angles.
• \(\angle BTA\cong\angle CTA\): True, as they are corresponding angles.
• \(\overline{AB}\cong\overline{CT}\): False. \(\overline{AB}\) corresponds to \(\overline{AC}\), not \(\overline{CT}\).

Answer:

\(\overline{AB}\cong\overline{CT}\) (the fourth option)