Use the image to answer the question.

Question

A scalene triangle with its base oriented nearly vertical is formed by the intersection of two lines and a line segment. A third line slopes upward from left to right and passes through the base of the triangle and its apex.

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)
Responses

CR←→
Modifying above upper C upper R with two-way arrow

DR←→
Modifying above upper D upper R with two-way arrow

QR←→
Modifying above upper Q upper R with two-way arrow

CD¯¯¯¯¯¯¯¯

Answer 1

In the scenario described, Lexi folded her paper such that point C is on top of point D, which indicates that the fold acts as a line of symmetry between these two points. The point E, where the fold intersects the line segment CD, serves as the midpoint.

Given that the fold line is a line of symmetry, the segment that bisects CD is the line segment QR, which is drawn through point E at an arbitrary angle. This means QR intersects CD at its midpoint, thus acting as the segment bisector for CD.

Therefore, the correct response is:

QR←→