Question

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 . She used a straight edge to draw R at an arbitray angle through point E. Finally, she drew CR through points C and R and DER through points D and R. Which line segment or line is the segment bisector in this scenario?
(1 point)

Answer 1

In this scenario, Lexi folded the paper such that point C was on top of point D, which means that the fold created a perpendicular bisector of the line segment CD at the intersection point, which we will call point E (the intersection point).

Since point R lies on the line drawn through point E at an arbitrary angle, and given that Lexi drew line segments CR and DR, the line segment CR and line segment DR are not guaranteed to bisect line segment CD unless R specifically lies on the perpendicular bisector of CD.

Thus, the segment bisector in this scenario is the fold itself, represented by the line that goes through point E, which is the midpoint of segment CD, making it the perpendicular bisector of CD.

To summarize, the segment bisector in this scenario is the line through point E that bisects the line segment CD.