Question

lexi 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) $overline{cd}$ $overleftrightarrow{dr}$ $overleftrightarrow{cr}$ $overleftrightarrow{qr}$

Explanation:

Step1: Recall segment - bisector definition

A segment bisector divides a line segment into two equal parts. When Lexi folded the paper so that point C was on top of point D, the fold line (which is the same as $\overleftrightarrow{QR}$) intersects $\overline{CD}$ at its mid - point E.

Step2: Identify the bisector

Since $\overleftrightarrow{QR}$ intersects $\overline{CD}$ at its mid - point E and divides $\overline{CD}$ into two equal parts (because of the folding operation), $\overleftrightarrow{QR}$ is the segment bisector of $\overline{CD}$.

Answer:

$\overleftrightarrow{QR}$