Question

ional information is required in order to know
the reason given.

1. sas
2. asa
3. aas
4. sss

Explanation:

Step1: Identify given congruent sides

We can see that $UT \cong KT$ (marked with double tick marks). Also, $\angle STU \cong \angle MTK$ because they are vertical angles.

Step2: Match requirement for SAS

For the SAS (Side-Angle-Side) congruence rule, we need two sides and the included angle of one triangle congruent to the corresponding parts of the other triangle. We already have one pair of sides and the included vertical angles. We need the other pair of sides that form the included angle: $ST \cong MT$.

Answer:

To use SAS congruence, we need $\boldsymbol{ST \cong MT}$ (the pair of sides that, along with the vertical angles and the given congruent sides, form the included angle for each triangle).