Question

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

Explanation:

Step1: Recall congruence rules

• 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.
• 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.

Step2: Analyze the given triangles

• We are given two angles (\(\angle T\) and \(\angle Q\)) and a non - included side (the side that is not between the two given angles. Here, the side \(PS = PQ\) (marked with one tick) is a non - included side with respect to the given angles \(\angle T\) and \(\angle Q\)).

Answer:

AAS