Question

which rule explains why these triangles are congruent? two triangles with markings and options: aas, sss, sas, asa, these triangles cannot be proven congruent.

Explanation:

To determine the congruence rule, we analyze the given triangles:

• In triangle \( TVU \) and \( WYX \) (assuming labels), we see two sides are marked equal (indicating two pairs of equal sides) and the included angle between these sides is marked equal (the angle at \( T \) and \( W \)).
• The SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
• AAS (Angle - Angle - Side) requires two angles and a non - included side, SSS (Side - Side - Side) requires three sides, and ASA (Angle - Side - Angle) requires two angles and the included side. Here, the pattern matches SAS as we have two sides and the included angle equal.

Answer:

SAS