Question

1. two congruent triangles are shown below. identify the corresponding parts of δabc and δrst that would be used to prove congruency using the sas congruence postulate. select all that apply. ∠b≅∠s, ac≅rt, ab≅rs, ∠a≅∠r (triangles: δabc with ab=7, ac=11, ∠a=56°; δrst with rs=7, rt=11, ∠r=56°)

Explanation:

To prove congruence using SAS (Side - Angle - Side), we need two sides and the included angle.

1. For side - angle - side:

• In \(\triangle ABC\) and \(\triangle RST\), we check the sides and the included angle.
• \(AB = 7\) and \(RS=7\), so \(AB\cong RS\).
• \(\angle A = 56^{\circ}\) and \(\angle R = 56^{\circ}\), so \(\angle A\cong\angle R\).
• \(AC = 11\) and \(RT = 11\), so \(AC\cong RT\).
• The option \(\angle B\cong\angle S\) is not part of the SAS for these triangles as \(\angle B\) and \(\angle S\) are not the included angles for the given sides.

Answer:

• \(AB\cong RS\)
• \(AC\cong RT\)
• \(\angle A\cong\angle R\)