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 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?

Answer 1

In this scenario, Lexi folded the paper such that point C was placed on top of point D. The fold creates a line that is the perpendicular bisector of the segment CD when the paper is unfolded. The intersection of this fold and the line segment CD is marked as point E.

Then, Lexi drew a line QR through point E at an arbitrary angle, and created lines CR and DR, where C and D are points on these lines.

The segment bisector in this context is the line that was formed by the fold, which intersects segment CD at point E. This line is not only the segment bisector of CD (since it divides CD into two equal lengths at E), but it also has the property of being perpendicular to CD at E.

To summarize, the segment bisector in this scenario is the fold line that intersects CD at point E. If QR is drawn at an arbitrary angle, it would not generally serve as a segment bisector unless it meets the criteria of bisecting CD. Hence, the key segment bisector is the fold line through E.