https://file.aiquickdraw.com/mathbot/file/17284924295580ar684ft.jpg

To correctly order the construction steps based on the image you provided, here is the proper sequence:

1. **Construct a circle with point \( D \) at the center with a radius \( \overrightarrow{DE} \).**
2. **Label point \( B \) at the other intersection of the circle and \( \angle CDE \).**
3. **Construct circles with points \( E \) and \( B \) at the centers, with each radius equal to \( \overrightarrow{EB} \).**
4. **Label the intersection of the circles just constructed \( A \) and \( F \).**
5. **Construct \( \overrightarrow{AF} \), which will be the angle bisector of \( \angle CDE \).**

This order outlines the logical steps of a geometric construction, starting with basic shapes and leading up to the final goal of bisecting the angle.

Would you like more details or explanations on any specific step?

Here are some related questions to consider:
1. What is the purpose of constructing circles with radius \( EB \) in such problems?
2. How does the intersection of two circles help in geometric constructions?
3. Why is bisecting an angle important in geometric constructions?
4. How does this type of construction apply to real-world scenarios?
5. What other geometric constructions involve circle intersections?

**Tip:** Always ensure that your compass is set carefully to maintain consistent radii when constructing multiple circles. This precision ensures accurate geometric results.

Place the steps of the construction in order: (1) Construct a circle with point D at the center with a radius DE. (2) Label point B at the other intersection of the circle and ∠CDE. (3) Construct AF which will be the angle bisector of ∠CDE. (4) Construct circles with points E and B at the centers, with each radius equal to EB. (5) Label the intersection of the circles just constructed A and F.

Learn how to place the steps of a geometric construction in the correct order. This problem focuses on constructing a circle with a given radius, labeling intersections, and using the angle bisector theorem. Suitable for students in Grades 9-10.

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