Question

complete the proof that \\(\overline{ux} \cong \overline{sw}\\).

statement	reason
2. \\(\overline{xy} \cong \overline{vw}\\)	given
3. \\(\angle y \cong \angle v\\)	given
4. \\(wy = xy + wx\\)	additive property of length
5. \\(vx = vw + wx\\)	additive property of length
6. \\(wy = vw + wx\\)	substitution
7. \\(vx = wy\\)
8. \\(\triangle swy \cong \triangle uxv\\)	asa
9. \\(\overline{ux} \cong \overline{sw}\\)	cpctc

Explanation:

Step1: Analyze Statements 5 and 6

From Statement 5: \( VX = VW + WX \) and Statement 6: \( WY = VW + WX \).

Step2: Apply Transitive Property

If two quantities are both equal to the same third quantity, they are equal to each other. So since \( VX = VW + WX \) and \( WY = VW + WX \), we can conclude \( VX = WY \) by the Transitive Property of Equality (or Substitution, but here it's the transitive property as both equal \( VW + WX \)).

Answer:

Transitive Property of Equality (or Substitution, recognizing both equal \( VW + WX \))