Question

the triangles are congruent by the sas congruence theorem. complete the congruence statements for the corresponding parts of the triangles. > move a choice into each space provided. \\( \angle b \cong \\) \\( \overline{a c} \cong \\) \\( \angle a \cong \\)

Explanation:

Step1: Identify congruent triangles

Since \(\triangle ABC\cong\triangle TRS\) (by SAS Congruence Theorem: \(AB = TR\), \(\angle B=\angle T\), \(BC = TS\)).

Step2: Find corresponding angles and sides

For \(\angle B\), in \(\triangle TRS\) the corresponding angle is \(\angle T\) (from the congruence \(\triangle ABC\cong\triangle TRS\)).
For \(\overline{AC}\), in \(\triangle TRS\) the corresponding side is \(\overline{RS}\) (by the order of congruence \(\triangle ABC\cong\triangle TRS\)).
For \(\angle A\), in \(\triangle TRS\) the corresponding angle is \(\angle R\) (from the congruence \(\triangle ABC\cong\triangle TRS\)).

Answer:

\(\angle B\cong\angle T\), \(\overline{AC}\cong\overline{RS}\), \(\angle A\cong\angle R\)