1. **State the problem:** We are given an equilateral triangle $\triangle TUV$ with points $X, Y, Z$ inside it forming smaller triangles. We need to complete the proof by ordering the given statements to show the relationships between the sides and angles. 2. **Recall definitions and properties:** - An equilateral triangle has all sides equal: $XY \cong YZ \cong ZX$ and $TU \cong UV \cong VT$. - Midpoints divide segments into equal parts. - SAS (Side-Angle-Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. - Corresponding parts of congruent triangles are congruent. 3. **Analyze the given segments:** - $TZ \cong ZU \cong UY \cong YV \cong VX \cong XT$ means these segments are equal, indicating points $X, Y, Z$ divide the sides into equal parts. 4. **Order the statements logically:** - First, since $\triangle TUV$ is equilateral, by definition: $$\text{(3) } C. \quad XY \cong YZ \cong ZX$$ - Next, the segments $TZ, ZU, UY, YV, VX, XT$ are equal by the midpoint or segment division property: $$\text{(2) } B. \quad TZ \cong ZU \cong UY \cong YV \cong VX \cong XT$$ - Then, the smaller triangles inside are congruent by SAS: $$\text{(3) } D. \quad \triangle TZX \cong \triangle UYZ \cong \triangle VZY$$ - Finally, corresponding angles of these congruent triangles are congruent: $$\text{(4) } A. \quad \angle T \cong \angle U \cong \angle V$$ 5. **Summary:** - $\triangle XYZ$ is equilateral (C). - The segments dividing the sides are equal (B). - The smaller triangles are congruent by SAS (D). - Corresponding angles are congruent (A). This completes the proof by ordering the statements as: C, B, D, A.