To prove the two triangles congruent using the SAS (Side-Angle-Side) postulate, we need to establish that two corresponding sides and the included angle between them are congruent in both triangles.
Based on the responses provided, we have:
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\(\angle UWK \cong \angle KMV\) - This provides a pair of congruent angles but does not help establish a side-length relationship.
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\(\angle VKM \cong \angle VUW\) - This also provides a pair of congruent angles.
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\(MK \cong WU\) - This establishes a pair of congruent sides but does not include an angle.
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\(VM \cong WV\) - This establishes another pair of congruent sides but does not include an angle.
To utilize SAS, you need:
- Two sides from each triangle that are congruent to each other.
- The angle that is included between those two sides must also be congruent.
Assuming that the angles provided are included between the corresponding sides, the additional piece of information needed here would be to establish one pair of sides as congruent along with the included angle.
Therefore, you would need either:
- One additional side is congruent to another, or
- One of the given angles to be established as an included angle between the pairs of congruent sides.
Thus, from the context of the options provided, the ideal response that would fulfill the condition for SAS is:
MK ≅ WU or VM ≅ WV plus the included angle ∠UWK ≅ ∠KMV or ∠VKM ≅ ∠VUW (which are not already covered).
Hence, any specific pair of corresponding sides along with one included angle that was not already matched to establish vindication of SAS would suffice.