The image shows two polygons on a grid, with the question asking whether the two figures are congruent. To determine congruence, we need to check if one figure can be transformed into the other using a combination of rigid transformations (translations, rotations, reflections). Congruent figures have the same size and shape, with corresponding sides and angles equal.

Analysis of the Figures:

• The red polygon is labeled $A, B, C, D, E, F$, and the purple polygon is labeled $G, H, I, J, K, L$.
• The number of sides and general shape of both polygons appear to match.
• The explanation in the provided text box suggests that a set of transformations (likely translation, rotation, or reflection) was applied, and the shapes lined up perfectly, indicating that the two figures are congruent.

Conclusion:

Yes, the two figures are congruent based on visual analysis and the information provided.

Would you like to go into more detail about the types of transformations, or do you have any other questions?

Here are 5 related questions to deepen your understanding:

1. What specific transformations were used to show the congruence of the two figures?
2. Can you describe how translation differs from rotation and reflection?
3. How would you prove congruence algebraically if the coordinates of the vertices were known?
4. How can you check whether the corresponding sides and angles of the two polygons are equal?
5. What role does the distance between corresponding vertices play in determining congruence?

Tip: When dealing with transformations, always remember that translation, rotation, and reflection do not change the size or shape of a figure, only its position or orientation.