Question

lea started with $overline{cd}$ 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 $overleftrightarrow{qr}$ at an arbitrary angle through point $e$. finally, she drew $overleftrightarrow{cr}$ through points $c$ and $r$ and $overleftrightarrow{dr}$ through points $d$ and $r$. which line segment or line is the segment bisector in this scenario? (1 point) $overline{cd}$ $overleftrightarrow{qr}$ $overleftrightarrow{dr}$ $overleftrightarrow{cr}$

Explanation:

Step1: Recall segment - bisector definition

A segment bisector divides a line segment into two equal parts. When Lei folded the paper so that point C was on top of point D, the fold line is the perpendicular bisector of segment $\overline{CD}$. The intersection of the fold and $\overline{CD}$ is point E.

Step2: Analyze the given lines

The line $\overleftrightarrow{QR}$ passes through the mid - point E of $\overline{CD}$. Since a line that passes through the mid - point of a line segment is a segment bisector of that line segment, $\overleftrightarrow{QR}$ bisects $\overline{CD}$. Lines $\overleftrightarrow{DR}$ and $\overleftrightarrow{CR}$ do not bisect $\overline{CD}$, and $\overline{CD}$ is the segment being bisected, not the bisector.

Answer:

$\overleftrightarrow{QR}$