which rule explains why these triangles are 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.
• 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.
• 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.
• SSS (Side - Side - Side): All three sides of one triangle are equal to all three sides of another triangle.

Step2: Analyze the given triangles

In triangles ( \triangle WVT) and ( \triangle UVT):

• We have (WV = UV) (marked with one tick), (WT=UT) (marked with one tick), and (\angle W=\angle U) (marked angles).
• This satisfies the AAS (Angle - Angle - Side) congruence rule as we have two angles ((\angle W) and (\angle U)) and a non - included side ((VT = VT) (common side)) equal.

Answer:

AAS