Question

which rule explains why these triangles are congruent? asa sss aas sas these triangles cannot be proven congruent.

Explanation:

Step1: Recall congruence rules

• 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.
• SSS (Side - Side - Side): All three sides of one triangle are equal to all three sides of another triangle.
• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Step2: Analyze the given triangles

• In \(\triangle TUQ\) and \(\triangle TSQ\), we have \(\angle U=\angle S\) (given as marked angles), \(TU = TS\) (marked with one tick), and \(TQ=TQ\) (common side).
• Here we have two angles (\(\angle U\) and \(\angle S\)) and a non - included side (\(TQ\)) that are equal.

Answer:

AAS