Answer true or false: a. All equilateral triangles are congruent. b. All equilateral triangles are similar.

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**Solution:**

1. **Part (a): "All equilateral triangles are congruent."**

- **Definition of Congruent:** Two figures are congruent if they have the same size and shape; that is, they must have equal corresponding side lengths and angles.
   - **Property of Equilateral Triangles:** In an equilateral triangle, all sides and all angles are equal. However, while all angles are $$60^\circ$$, the side lengths can vary.
   - **Conclusion:** Since equilateral triangles can have different side lengths, they do not necessarily have the same size. Therefore, they are not all congruent.
   
   **Answer to (a): False**

2. **Part (b): "All equilateral triangles are similar."**

- **Definition of Similarity:** Two figures are similar if they have the same shape, meaning their corresponding angles are equal and their corresponding sides are in proportion.
   - **Property of Equilateral Triangles:** Every equilateral triangle has angles of $$60^\circ$$. Regardless of the side lengths, the ratio of any two corresponding sides between any two equilateral triangles is constant.
   - **Conclusion:** All equilateral triangles have the same angles and their sides are in proportion, which means they are all similar.
   
   **Answer to (b): True**
a. False b. True

Answer true or false: a. All equilateral triangles are congruent. b. All equilateral triangles are similar.

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