To apply the SAS (Side-Angle-Side) Congruency Theorem, you need to ensure that you have two sides and the included angle of one triangle congruent to the corresponding two sides and the included angle of the other triangle.
From the information provided:
- You have \( UL \cong WV \) (one pair of sides),
- \( UW \cong VL \) (the second pair of sides),
- \( \angle L \cong \angle W \) (the included angle).
To use the SAS Congruency Theorem, you must ensure that the angle is included between the two pairs of congruent sides.
- Confirm that \( \angle L \) is between sides \( UL \) and \( UW \) in triangle \( UWL \).
- Confirm that \( \angle W \) is between sides \( WV \) and \( VL \) in triangle \( WVL \).
Since you provided that \( \angle L \cong \angle W \), if \( \angle L \) is indeed between \( UL \) and \( UW \), and \( \angle W \) is between \( WV \) and \( VL \), you have met all the requirements of the SAS theorem.
Thus, the additional information needed is to affirm the positions of the angles in relation to the sides (i.e., confirmation of which angle is included between the respective congruent sides).
In summary, the necessary additional detail needed is to confirm that:
- \(\angle L\) is the included angle between sides \( UL \) and \( UW \)
- \(\angle W\) is the included angle between sides \( WV \) and \( VL \)
This will provide sufficient information to conclude that the triangles are congruent by the SAS Congruency Theorem.
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