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Olena can indeed finish constructing the perpendicular bisector despite losing her compass. In the diagram, she has already drawn two intersecting arcs above the line segment \( \overline{AB} \), which is sufficient to complete the construction.

### Explanation:
- The intersection points of the arcs determine the line that is perpendicular to \( \overline{AB} \) and bisects it.
- To complete the construction, Olena only needs to draw a straight line through these two intersection points. This line will be the perpendicular bisector of \( \overline{AB} \).
- A compass is not necessary for this final step; she can use a straightedge to connect the intersection points.

The correct answer is:

**Yes, because the only step left is to draw a line that passes through the intersection of the arcs and is perpendicular to line \( \overline{AB} \), which Olena can accomplish with a straightedge.**

### Additional Questions:
1. What would Olena need the compass for if she hadn't drawn the arcs yet?
2. How is the perpendicular bisector useful in geometric constructions?
3. Can you explain why the perpendicular bisector divides \( \overline{AB} \) into two equal halves?
4. What role do the arcs above and below the line play in constructing a bisector?
5. What are other methods for constructing a perpendicular bisector without a compass?

### Tip:
Always ensure you have identified the key points of intersection when constructing perpendicular bisectors, as these are critical to completing the construction with a straightedge.

Olena started constructing a perpendicular bisector for line segment AB. Her progress is shown. Olena lost her compass. Can she finish constructing the perpendicular bisector? Explain.

Explore how Olena can complete the construction of a perpendicular bisector for line segment AB even after losing her compass. Learn key geometric concepts, including the perpendicular bisector theorem, and understand how to use a straightedge to finish the construction. Suitable for Grades 7-10.

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