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. $\angle b\cong$ $\overline{ac}\cong$ $\angle a\cong$ $\angle c\cong$

Explanation:

Step1: Determine the corresponding angles and sides

Since \(\triangle ABC\cong\triangle TSR\) (by SAS Congruence Theorem: \(AB = TS\), \(\angle B=\angle T\), \(BC = TR\)), we can find the corresponding parts.

• For \(\angle B\): Corresponding angle is \(\angle T\) (as per the congruence of triangles \(\triangle ABC\) and \(\triangle TSR\) where the angle - side - angle correspondence is considered).
• For \(\overline{AC}\): Corresponding side is \(\overline{RS}\) (by the property of congruent triangles, sides opposite to equal angles or in the congruent structure).
• For \(\angle A\): Corresponding angle is \(\angle R\) (using the congruence relation of the two triangles).
• For \(\angle C\): Corresponding angle is \(\angle S\) (based on the congruence of \(\triangle ABC\) and \(\triangle TSR\)).

Answer:

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