https://r2.erweima.ai/mathbot/image/1726774788490k27z85pa.jpg

The exercise in the image is a geometric construction task, asking to reflect points and shapes based on certain lines of symmetry. Here is a breakdown of the requirements based on the text:

1. **Reflect point A over line (ds)**:
   - Reflect point A across line \( ds \). You will create a new point that is symmetric to A with respect to line \( ds \).

2. **Reflect point B over line (ds)**:
   - Perform the same reflection for point B over the line \( ds \), resulting in point \( B' \), symmetric to B.

3. **Reflect point C over axis (dl)**:
   - Reflect point C across the axis \( dl \) (which is perpendicular to line \( ds \)) to form its symmetric counterpart, \( C' \).

4. **Reflect point D over line (ds)**:
   - Repeat the reflection process for point D, reflecting it over \( ds \) to create \( D' \).

5. **Reflect point E and F**:
   - Reflect point E over line \( ds \) to form point \( E' \), and similarly for point F to create \( F' \).

6. **Reflect the shapes**:
   - Reflect the geometric shapes (polygon, square, and circle) over line \( ds \). This involves reflecting each vertex of the shapes across the line.

### Tip:
When performing reflections, use a compass and straightedge to ensure precision. For each point, measure the perpendicular distance from the line of symmetry and recreate that distance on the opposite side.

Would you like further clarification on any of these steps, or would you like me to go into more details? 

Here are 5 questions for further practice:
1. How do you find the reflection of a point across a line geometrically?
2. Can you explain the process of reflecting a polygon across a line?
3. What are the properties of symmetrical shapes in terms of their orientation after reflection?
4. How do you construct perpendicular lines from a point to a line?
5. How can you verify the accuracy of the reflected points and shapes?

Tip: Always ensure that the reflected point is the same distance from the line as the original point, but on the opposite side.

Using your geometric tools, perform the following constructions:
- Reflect point A over line (ds).
- Reflect point B over line (ds).
- Reflect point C over line (dl).
- Reflect point D using the symmetry of line (ds).
- Reflect point E to create a symmetric counterpart E' over line (ds).
- Reflect point F to create a symmetric counterpart F' over line (ds).
Also, reflect all shapes with respect to line (ds).

Learn how to perform geometric reflections over symmetry lines. Reflect points A, B, C, D, E, F, and various shapes with respect to line (ds). This step-by-step solution explains geometric concepts like symmetry and reflection theorem. Suitable for students in Grades 7-9.

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