Lexi started with CD¯¯¯¯¯¯¯¯ on her paper. She folded her paper so that point C was on top of point D . Then, she unfolded her paper and labeled the intersection of the fold and the line segment with point E .​ She used a straight edge to draw QR←→ at an arbitrary angle through point E . Finally, she drew CR←→ through points C and R and DR←→ through points D and R . Which line segment or line is the segment bisector in this scenario? (1 point) Responses CD¯¯¯¯¯¯¯¯ Modifying above upper C upper D with bar CR←→ Modifying above upper C upper R with two-way arrow DR←→ Modifying above upper D upper R with two-way arrow QR←→

1 answer

In this scenario, Lexi started with the line segment \(CD\) and folded the paper such that point \(C\) was on top of point \(D\). The point of intersection of the fold and the line segment \(CD\) is labeled as point \(E\). By folding \(C\) on top of \(D\), it implies that point \(E\) is the midpoint of segment \(CD\), making the fold the perpendicular bisector of line segment \(CD\).

After unfolding, Lexi draws a line \(QR\) through point \(E\), and then lines \(CR\) and \(DR\) through points \(C, R\) and \(D, R\) respectively.

Since point \(E\) is the midpoint of segment \(CD\) due to the folding, and lines \(CR\) and \(DR\) are derived from points \(C\) and \(D\) respectively stretching through point \(R\), the line segment or line that acts as the perpendicular bisector of \(CD\) in this construction is the fold itself.

Therefore, the correct answer in terms of bisector property is:

\(CD\) (with a bar over it, indicating it is a segment).