Question

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

Explanation:

Step1: Identify vertical angles

$\angle TSU$ and $\angle VSW$ are vertical angles. Vertical angles are equal, so $\angle TSU=\angle VSW$.

Step2: Analyze given side - side information

We are given that $TS = WS$ (marked with one tick) and $US = VS$ (marked with two ticks).

Step3: Apply the SAS (Side - Angle - Side) congruence rule

In $\triangle TSU$ and $\triangle WSV$, we have two sides and the included angle equal. That is, $TS = WS$, $\angle TSU=\angle VSW$, and $US = VS$.

Answer:

SAS