Question

1. δwxy ≅ δuvy (given)
2. ux ≅ vw (cpctc)
3. uv ≅ wx (cpctc)
4. wy ≅ xy (cpctc)
5. ∠uyv ≅ ∠wvy (cpctc)
6. uw = uy + wy (additive property of length)
7. ux = vy + uy (additive property of length)
8. uw = vy + xy (substitution)
9. uw = vx (transitive property of equality)
10. blank for statement

Explanation:

Step1: Analyze the Proof Structure

We have a proof involving congruent triangles (\(\triangle XWY \cong \triangle UVY\) given) and are using CPCTC (Corresponding Parts of Congruent Triangles are Congruent) and properties of length. The goal is to find the final statement, likely about segment congruence or equality.

Step2: Trace the Logic

From steps 6 - 9, we establish \(UW = VX\) (step 9, Transitive Property). Since \(UW\) and \(VX\) are sides, and we have congruent triangles, the final statement should be \(\overline{UW} \cong \overline{VX}\) (or \(UW = VX\) as a segment equality, but congruence of segments is typical here).

Answer:

\(\overline{UW} \cong \overline{VX}\) (or \(UW = VX\) as a segment congruence/equality statement)