Let's break down the explanation step by step:
1. Angle A:
- Given that ATUV and AWVU are triangles.
- Both triangles have the angle A in common.
2. Side TU and WV:
TU and WV are given to be congruent sides.
3. Angle T and Angle W:
- The triangles have another pair of congruent angles, T and W.
4. ASA Congruence Theorem:
- By the Angle-Side-Angle (ASA) congruence theorem, if two triangles have two congruent angles and the included side is congruent, then the triangles are congruent.
5. Conclusion:
- Therefore, triangle ATUV cong triangle AWVU, and corresponding parts are equal, including AT = AW.
In summary, the Angle-Side-Angle congruence theorem justifies that the given triangles are congruent, leading to the conclusion that ATUV equals the same AWVU