Question

here are two triangles. which statement is true? △tsu≌△rsu by the asa congruence postulate. △tsu≌△rsu by the aas congruence theorem. △tsu≌△rsu by the hl congruence theorem. there is not enough information to conclude that the triangles are congruent.

Explanation:

Step1: Identify the given information

We have two triangles \(\triangle TSU\) and \(\triangle RSU\). \(ST = SR\) (marked with one - tick), \(\angle T=\angle R\) (marked with one - arc), and \(SU = SU\) (common side).

Step2: Recall the congruence theorems

• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.
• HL (Hypotenuse - Leg): Applies to right - angled triangles.

In \(\triangle TSU\) and \(\triangle RSU\), we have \(\angle T=\angle R\), \(ST = SR\), and \(\angle TUS=\angle RUS\) (vertical angles are equal). The side \(SU\) is a non - included side with respect to the two angles \(\angle T\) and \(\angle TUS\) (in \(\triangle TSU\)) and \(\angle R\) and \(\angle RUS\) (in \(\triangle RSU\)).

Answer:

\(\triangle TSU\cong\triangle RSU\) by the \(AAS\) congruence theorem.