1. **State the problem:** We need to complete the proof that $\triangle VYZ \cong \triangle WXZ$ given that $\triangle VWZ$ and $\triangle XYZ$ are equilateral triangles. 2. **Recall given information:** - $\triangle VWZ$ is equilateral. - $\triangle XYZ$ is equilateral. - From these, we know $VZ \cong WZ$ and $XZ \cong YZ$ because all sides in equilateral triangles are equal. - Also, $\angle VZY \cong \angle WZX$ by the Vertical Angle Theorem. 3. **Step 6: Identify the next congruent parts and reason:** - Statement: $YZ \cong XZ$ - Reason: Sides opposite equal angles in equilateral triangles are equal (or by the definition of equilateral triangles, all sides are equal). 4. **Step 7: Use a congruence postulate to conclude:** - Statement: $\triangle VYZ \cong \triangle WXZ$ - Reason: Side-Angle-Side (SAS) Postulate, since we have two pairs of sides and the included angle congruent. Thus, the completed proof steps 6 and 7 are: 6. $YZ \cong XZ$ Reason: Definition of equilateral triangle (all sides equal). 7. $\triangle VYZ \cong \triangle WXZ$ Reason: SAS Postulate. Final answer: $\triangle VYZ \cong \triangle WXZ$ by SAS.