The image shows a question about transformations of a geometric figure composed of identical equilateral triangles, each with three congruent sides and 60° angles. The problem involves understanding rotations about different points in the figure.

Let's go through each part of the question:

1. A) Rotating 60° clockwise about $E$ maps $B$ onto $F$.

   • Rotating 60° clockwise about point $E$, which is the center of the adjacent equilateral triangles, brings point $B$ to $F$.

2. B) Rotating 60° clockwise about $H$ maps $B$ onto $K$.

   • Rotating 60° clockwise about $H$, which is at the bottom-left of the figure, moves point $B$ to $K$.

3. C) Rotating 60° counterclockwise about $K$ maps $C$ onto $B$.

   • A 60° counterclockwise rotation about $K$ moves $C$ to $B$, as observed geometrically.

4. D) Rotating 120° clockwise about $F$ maps $CG$ onto $GE$.

   • A 120° clockwise rotation about $F$ moves segment $CG$ (right diagonal of the triangle) onto $GE$.

5. E) Rotating 120° clockwise about $B$ maps $CG$ onto $FG$.

   • A 120° clockwise rotation about $B$ moves $CG$ to $FG$, maintaining alignment with the geometry.

6. F) Rotating 60° clockwise about $D$ maps $\triangle DEA$ onto $\triangle DEH$.

   • A 60° clockwise rotation about $D$ shifts $\triangle DEA$ (leftmost triangle) to $\triangle DEH$ below it.

7. G) Rotating 180° clockwise about $F$ maps $\triangle BEF$ onto $\triangle CGE$.

   • A 180° rotation about $F$ moves $\triangle BEF$ to $\triangle CGE$, as $F$ remains the fixed center.

Do you want me to provide a detailed geometric explanation for any part or help with further questions?

Here are five related questions to expand your understanding:

1. What happens if we rotate 90° instead of 60° in similar diagrams?
2. How do rotations affect the orientation of specific line segments in equilateral triangles?
3. Can you use reflections instead of rotations to map one segment to another?
4. How can we verify rotations using coordinate transformations?
5. What is the difference between clockwise and counterclockwise rotations for the same angle?

Tip: Always identify the center of rotation and the direction (clockwise or counterclockwise) to simplify the problem.