1. **Problem statement:** Identify the similar triangles in each part and provide the reason for similarity. Show the proportions used. --- ### a) $\triangle ABC \cong \triangle DBC$ by SAS similarity 2. **Reasoning:** Both triangles share side $BC$, and two pairs of sides are proportional with the included angle equal. 3. **Proportions:** If $AB$ and $DB$ are corresponding sides, and $AC$ and $DC$ are corresponding sides, then $$\frac{AB}{DB} = \frac{AC}{DC}$$ with the included angle at $B$ congruent. --- ### b) $\triangle XYZ \cong \triangle IHZ$ by AAA similarity 4. **Reasoning:** All three corresponding angles are equal. 5. **Proportions:** Corresponding sides are proportional: $$\frac{XY}{IH} = \frac{YZ}{HZ} = \frac{XZ}{IZ}$$ --- ### c) $\triangle ABC \cong \triangle AED$ by SSS similarity 6. **Reasoning:** All three pairs of corresponding sides are proportional. 7. **Proportions:** Given sides, $$\frac{AB}{AE} = \frac{BC}{ED} = \frac{AC}{AD}$$ where the side lengths are 22.5, 18, 12, 15, and 8 as labeled in the diagram. --- **Final answers:** - a) $\triangle ABC \cong \triangle DBC$ by SAS similarity with $\frac{AB}{DB} = \frac{AC}{DC}$ - b) $\triangle XYZ \cong \triangle IHZ$ by AAA similarity with $\frac{XY}{IH} = \frac{YZ}{HZ} = \frac{XZ}{IZ}$ - c) $\triangle ABC \cong \triangle AED$ by SSS similarity with $\frac{AB}{AE} = \frac{BC}{ED} = \frac{AC}{AD}$