In the case of similar triangles, certain properties must always be true. The key characteristics of similar triangles are:

1. Same shape but not necessarily the same size: Similar triangles are proportional in size, meaning their corresponding angles are equal, but the side lengths may differ.
2. Corresponding angles are congruent: One of the defining features of similar triangles is that their corresponding angles are always equal.

Based on this, the two correct statements about the triangles in the design are:

• C. They are the same shape, but not necessarily the same size.
• E. They have corresponding angles that are congruent.

Do you want further details or have any questions?

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Five related questions:

1. What are the key differences between similar and congruent triangles?
2. How can you prove that two triangles are similar?
3. What does it mean for two sides to be proportional in similar triangles?
4. How do you calculate the missing side of a triangle using proportions in similar triangles?
5. Can a right triangle be similar to a non-right triangle?

Tip: In similar triangles, the ratio of corresponding sides remains constant, which is useful for solving problems involving unknown side lengths.