Which of the following sets of shapes are NOT all similar to each other? (A) right triangles (B) spheres (C) \( 30-60-90 \) triangles (D) squares (E) cubes

To determine which set of shapes is **not** entirely composed of similar figures, let's analyze each option: 1. **Right Triangles (Option A):** - **Similarity Criteria:** Two triangles are similar if their corresponding angles are equal and their sides are proportional. - **Analysis:** All right triangles share one 90-degree angle, but the other two angles can vary. For example, a \(45-45-90\) triangle is **not** similar to a \(30-60-90\) triangle because their acute angles differ. - **Conclusion:** **Not all right triangles are similar**. 2. **Spheres (Option B):** - **Similarity Criteria:** All spheres are similar because they share the same shape; the only difference is their size. - **Conclusion:** **All spheres are similar**. 3. **\(30-60-90\) Triangles (Option C):** - **Similarity Criteria:** These triangles have the same set of angles (\(30^\circ\), \(60^\circ\), \(90^\circ\)), ensuring similarity. - **Conclusion:** **All \(30-60-90\) triangles are similar**. 4. **Squares (Option D):** - **Similarity Criteria:** All squares have equal sides and equal angles (\(90^\circ\)), making them similar through dilation. - **Conclusion:** **All squares are similar**. 5. **Cubes (Option E):** - **Similarity Criteria:** All cubes have equal edge lengths and identical faces, ensuring similarity. - **Conclusion:** **All cubes are similar**. **Final Answer:** **A) right triangles**