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?
Options
CR
QR
DR
CD
In this scenario, the line segment that is the segment bisector is QR.
In this scenario, the segment bisector is line segment CR.
To determine which line segment or line is the segment bisector in this scenario, we need to understand the concept of a segment bisector.
A segment bisector is a line segment, line, or ray that divides a given segment into two congruent parts. In other words, it cuts the segment into two equal halves.
In Lexi's scenario, she first folded her paper so that point C was on top of point D. Then, she unfolded the paper and labeled the intersection of the fold and the line segment with point E.
Next, she drew QR←→ at an arbitrary angle through point E.
Finally, she drew CR←→ through points C and R and DR←→ through points D and R.
To determine the segment bisector, we need to identify whether any of these lines divides the segment CD¯¯¯¯¯¯¯¯ into two congruent parts.
Looking at the lines, we can see that line CR←→ passes through both points C and R, but it does not intersect segment CD¯¯¯¯¯¯¯¯. Therefore, CR←→ is not the segment bisector.
Line QR←→ passes through point E, which is the intersection of the fold and segment CD¯¯¯¯¯¯¯¯. This means that QR←→ effectively divides CD¯¯¯¯¯¯¯¯ into two equal parts, namely CE¯¯¯¯¯¯¯¯ and DE¯¯¯¯¯¯¯¯. Hence, QR←→ is the segment bisector in this scenario.
Therefore, the correct answer is QR.