To prove the two triangles congruent using the Side-Angle-Side (SAS) postulate, you need to show that two sides and the angle included between them are congruent in both triangles.
Based on the responses provided:
- ∠UWK ≅ ∠KMV (Angle)
- MK¯¯¯¯¯¯¯¯¯¯ ≅ WU¯¯¯¯¯¯¯¯¯ (Side)
- VM¯¯¯¯¯¯¯¯¯ ≅ WV¯¯¯¯¯¯¯¯¯ (Side)
- ∠VKM ≅ ∠VUW (Angle)
From the information given, you have:
- One pair of angles: ∠UWK ≅ ∠KMV.
- Two pairs of sides: MK ≅ WU and VM ≅ WV.
However, to satisfy the SAS condition specifically, you need one angle to be between the two sides.
Thus, the additional piece of information needed to complete the proof of triangle congruence using SAS is the congruence of angles that is included between the two pairs of sides already given. The option that provides that information is:
∠VKM ≅ ∠VUW
This angle is between the sides MK and VM and will support using the SAS criterion to prove the triangles congruent.