For triangles to be considered similar, certain properties must be true. Based on the definitions and properties of similar triangles, the correct answers are:

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

Explanation:

• C: Similar triangles have the same shape because their corresponding angles are congruent, but they can differ in size, meaning their corresponding sides are proportional, not necessarily equal.
• E: One key property of similar triangles is that their corresponding angles are always congruent.

Incorrect Options:

• A: This is incorrect because the triangles are not necessarily the same size (they may be proportional in size).
• B: This is incorrect because similar triangles do not have to be the same size, just the same shape.
• D: This is incorrect because similar triangles have proportional corresponding sides, not necessarily congruent ones.

Would you like further details or have any questions?

Here are 5 related questions to think about:

1. How can you prove two triangles are similar using angle relationships?
2. What is the difference between congruent and similar triangles?
3. Can two triangles be similar if only one pair of corresponding angles is congruent?
4. What is the relationship between the sides of two similar triangles?
5. How does the concept of similarity apply to real-world problems like scaling models?

Tip: When working with similar triangles, always check both the angles (for congruence) and the sides (for proportionality).