Questions: 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) CR CD DR QR

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)
CR
CD
DR
QR

Transcript text: Lexi started with $\overline{C D}$ 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 $\overleftrightarrow{Q R}$ at an arbitrary angle through point $E$. Finally, she drew $\overleftrightarrow{C R}$ through points $C$ and $R$ and $\overleftrightarrow{D R}$ through points $D$ and $R$. Which line segment or line is the segment bisector in this scenario? (1 point) $\overleftrightarrow{C R}$ $\overline{C D}$ $\overleftrightarrow{D R}$ $\overleftrightarrow{Q R}$

Solution

Solution Steps

Step 1: Understand the Problem

Lexi started with line segment 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 line with line segment CD as 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. The question asks which line segment or line is the segment bisector in this scenario.

Step 2: Identify Key Information

Line segment CD is given.
Point E is the midpoint of CD because the paper was folded such that C coincides with D.
QR is drawn through point E.
CR and DR are drawn through points C, R, and D, R respectively.

Step 3: Determine the Segment Bisector

Since point E is the midpoint of CD, any line passing through E and intersecting CD will bisect CD. In this case, QR passes through E and intersects CD.