Final Answer:
The statement to be proven is that triangle TUW is congruent to triangle STV.
Step-by-step explanation:
To prove this congruence, we can use the following information:
1. T is the midpoint of SU and TW: This implies that ST = TU = UW.
2. SV ≅ TV and TV ≅ UV: These are given as congruent.
Now, considering the sides and angles, we can see that STU and SVT share the same side lengths due to the midpoint property. Additionally, the congruence of TV and UV ensures the angles are equal. Therefore, by the Side-Angle-Side (SAS) congruence criterion, triangle TUW is congruent to triangle STV.
This proof relies on the fundamental properties of midpoints and congruent line segments, highlighting the geometric principles that support the congruence of the two triangles. The conclusion, based on these properties, solidifies the congruent relationship between triangles TUW and STV.