Figure BCDEF 
 congruent to Figure GHIJK because rigid motions 
 be used to map Figure BCDEF onto Figure GHIJK.

Figure BCDEF 
 similar to Figure GHIJK because rigid motions and/or dilations 
 be used to map Figure BCDEF onto Figure GHIJK.

It looks like you are working on a geometric problem involving congruence and similarity of two figures, BCDEF and GHIJK. Let’s break it down:

1. **Congruence:**  
   Two figures are congruent if one can be transformed into the other using only rigid motions (transformations that preserve size and shape), such as:
   - **Translation** (sliding the figure without rotating it),
   - **Rotation** (spinning the figure around a point),
   - **Reflection** (flipping the figure over a line).

   Therefore, **Figure BCDEF is congruent to Figure GHIJK** because rigid motions can be used to map Figure BCDEF onto Figure GHIJK without changing the size or shape of the figure.

2. **Similarity:**  
   Two figures are similar if one can be transformed into the other using a combination of rigid motions and dilations (scaling the figure larger or smaller while keeping the same proportions). A dilation allows for a change in size while maintaining the shape.

   Therefore, **Figure BCDEF is similar to Figure GHIJK** because a combination of rigid motions and/or dilations can be used to map Figure BCDEF onto Figure GHIJK, meaning their shapes are the same but their sizes might differ.

### Do you want any further details or clarifications on this?

Here are 5 related questions for further practice:
1. What transformations are classified as rigid motions?
2. How do you determine if two figures are similar using transformations?
3. Can two congruent figures also be similar? Why or why not?
4. What role does dilation play in transforming figures?
5. How do you prove two figures are congruent using transformations?

**Tip:** When determining similarity, always check both the angles (which must be equal) and the side lengths (which must be proportional).

Figure BCDEF congruent to Figure GHIJK because rigid motions be used to map Figure BCDEF onto Figure GHIJK. Figure BCDEF similar to Figure GHIJK because rigid motions and/or dilations be used to map Figure BCDEF onto Figure GHIJK.

Understand how Figures BCDEF and GHIJK are congruent and similar through the use of rigid motions and dilations. Explore key concepts like congruence, similarity, and transformation rules in geometry, suitable for students in Grades 8-10.

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