The problem asks to select shapes that can be formed by a single reflection of shape $X$.

Solution:

1. Identify Shape $X$: Shape $X$ looks like an "L" flipped horizontally with a horizontal bar on the top and a vertical bar on the left.

2. Reflection Options:

   • A shape can be reflected vertically, horizontally, or along the diagonal lines.

3. Analyze Each Shape:

   • Shape A: Looks like a reflection over a vertical line. (Match)
   • Shape B: This shape is a vertical flip of shape $X$. (No Match)
   • Shape C: Rotated but not reflected. (No Match)
   • Shape D: Similar to shape $X$ but shifted. (No Match)
   • Shape E: A vertical reflection of shape $X$. (Match)
   • Shape F: Similar to shape $X$ but not a reflection. (No Match)
   • Shape G: Horizontal reflection of shape $X$. (Match)
   • Shape H: Shape similar to shape $X$ but flipped vertically. (No Match)

Shapes that match with a single reflection of $X$: A, E, and G.

Would you like more details or have any questions?

Follow-up Questions:

1. What types of reflections are possible in geometric transformations?
2. How does rotation differ from reflection in transformations?
3. What is the effect of reflecting a shape over a diagonal line?
4. How would shape $X$ look if rotated by 90 degrees?
5. What methods can be used to distinguish between reflection and rotation?

Tip: When identifying reflections, look for mirror symmetry across a specific axis!