1. **State the problem:** We are given two triangles, $\triangle ABC$ and $\triangle DEF$, with $\angle A \cong \angle D$. The sides including these angles are $AB = 6$ cm, $AC = 9$ cm, $DE = 4$ cm, and $DF = 6$ cm. We need to determine which statement best shows that $\triangle ABC \sim \triangle DEF$. 2. **Recall the SAS Similarity Theorem:** If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar. 3. **Check the ratios of the sides including the given angles:** $$\frac{AB}{DE} = \frac{6}{4} = 1.5$$ $$\frac{AC}{DF} = \frac{9}{6} = 1.5$$ 4. **Since the ratios of the two pairs of sides are equal and the included angles $\angle A$ and $\angle D$ are congruent, by the SAS Similarity Theorem, the triangles are similar.** 5. **Evaluate the other options:** - Option B requires two pairs of angles congruent, which is not given. - Option C requires all three pairs of sides proportional, but only two pairs are given. - Option D claims congruence, but the sides are not all equal. **Final answer:** Option A is correct. $$\boxed{\text{Two pairs of corresponding sides are proportional, and the included angles are congruent, so the triangles are similar by SAS Similarity Theorem.}}$$