https://file.aiquickdraw.com/mathbot/file/1727285870622tzh379t1.jpg

From the image provided and analyzing the shapes of the figures:

1. **Triangle D' is congruent to Triangle D**: This is true if the triangles D and D' have the same shape and size. Based on the visual, they appear to be similar in proportion and orientation, implying congruence.

2. **Figure C translated to Figure D' and Figure D translated to Figure C'**: This statement implies a translation (a type of transformation that slides a figure to a new position without altering its shape or orientation) between these figures. Observing the figures, it is clear that neither C nor D appears to match D' or C' through a simple translation. The orientations and positions suggest more complex transformations, possibly involving rotation or reflection.

3. **Figure C is not congruent to Figure C'**: This is true. Visually, C and C' are different in both size and shape. Figure C is a larger trapezoid, while C' is a smaller triangle, indicating they are not congruent.

4. **Triangle C is congruent to Triangle C'**: This is false. There is no triangle labeled C; the figure labeled C is a trapezoid, and C' is a triangle.

Based on the assessment, the true statements would be:
- Triangle D' is congruent to Triangle D.
- Figure C is not congruent to Figure C'.

Would you like further details on any particular aspect of this analysis, or do you have any other questions?

Here are some related questions you might consider:
1. What defines congruence between two geometric figures?
2. How can you determine if two figures are related by translation, rotation, or reflection?
3. What is the difference between congruence and similarity in geometry?
4. Could there be any transformations that might make C' congruent or similar to C?
5. How do translations affect the properties of geometric shapes?

Tip: Always verify congruence by comparing side lengths and angles using geometric tools or calculations when precise accuracy is needed.

Select all the true statements about transformations and congruence between the shapes shown in the image.

Analyze congruence and transformations between triangles and geometric shapes in this problem. Identify whether figures are congruent based on size and orientation, and determine if the transformations are valid. Suitable for students in Grades 6-8.

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