1. **Problem Statement:** Determine whether the triangles in problem 9 are similar by AA~, SSS~, SAS~, or not similar. 2. **Given:** Two triangles connected by segment UW with angles 72° at TUW and UVW. 3. **Step 1: Identify corresponding angles and sides.** - Triangle TUW has angle $\angle TUW = 72^\circ$. - Triangle UVW has angle $\angle UVW = 72^\circ$. 4. **Step 2: Check for Angle-Angle (AA) similarity.** - If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar by AA. - Since both triangles share angle $72^\circ$ and segment UW is common, check if another pair of angles are equal. 5. **Step 3: Use the fact that the sum of angles in a triangle is $180^\circ$.** - If $\angle TUW = 72^\circ$ and $\angle UVW = 72^\circ$, check the other angles. 6. **Step 4: If two angles match, triangles are similar by AA.** 7. **Conclusion:** Since both triangles have an angle of $72^\circ$ and share side UW, and assuming the other corresponding angles are equal (as per the problem's diagram), the triangles are similar by AA~. **Final answer:** The triangles are similar by AA~.