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The problem shows two figures (A and B) where different transformations are applied to two triangles, C and D, within the figure. Let's break down the information:

1. **Figure A** shows two triangles, C (yellow) and D (green), arranged to form a rectangle.
2. **Figure B** is created by translating Triangle C to a new position (C') and then translating Triangle D to a new position (D').

We are asked to identify which statements are true among the following options:

- **(A)** Figure A is congruent to Figure B.
- **(B)** Figure B is a translation of Figure A.
- **(C)** Triangle C' is congruent to Triangle C.
- **(D)** Triangle D' is congruent to Triangle D.

### Analyzing the Options:

- **Option A**: Figure A is not congruent to Figure B because in Figure B, Triangle D is translated downward, and Figure B overall does not form a rectangle like Figure A. Thus, **this is false**.
  
- **Option B**: Figure B is not simply a translation of Figure A. Triangles C and D were individually translated to new positions, but the entire figure has changed form. So, **this is false**.

- **Option C**: Triangle C is translated to a new position (C'), and no change is made to its size or shape. Therefore, Triangle C' is congruent to Triangle C. **This is true**.

- **Option D**: Triangle D is similarly translated to a new position (D'), and again, its size and shape remain the same. Triangle D' is congruent to Triangle D. **This is true**.

### Conclusion:
The true statements are **(C)** and **(D)**.

Would you like further details or clarification on any part of this explanation?

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Here are five related questions to deepen understanding:
1. What is the definition of congruence in geometry?
2. How does translation affect the shape and orientation of geometric figures?
3. Can a figure that undergoes rotation still be congruent to the original figure?
4. Why doesn't Figure A remain congruent to Figure B after individual translations of triangles?
5. What are other types of transformations besides translation?

**Tip**: Always remember that translations preserve the size and shape of geometric figures, meaning they stay congruent to their original versions.

Clare created Figure A. Then she created Figure B by translating Triangle C and then translating Triangle D. Which of the statements are true regarding the figures and triangles?

Explore a geometry problem involving translation and congruence of triangles. Understand how translations affect the positions of triangles while maintaining their congruence. Suitable for students in Grades 6-8.

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