Question

Question

Use the image to answer the 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

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

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

CD¯¯¯¯¯¯¯¯
Modifying above upper C upper D with bar

QR←→
Modifying above upper Q upper R with two-way arrow
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Answer 1

To determine which line segment or line is the segment bisector in this scenario, we first need to understand the context given:

1. Lexi folds her paper so that point C aligns with point D, meaning that CD represents the line segment being bisected.
2. The intersection point E occurs at the fold, and Lexi then draws QR through E.
3. The lines CR and DR are drawn through points C, D, and R, respectively.

Given that a segment bisector divides a segment into two equal parts, and since Lexi has folded the paper so points C and D overlap, it suggests that segments CR and DR are involved in this bisecting action.

Since CD is the segment formed by C and D, and the fold indicates that E is the midpoint of CD:

• CD is the segment being bisected, while E serves as the midpoint.

Consequently, the segment bisector that divides CD into two equal segments can be identified as:

QR ←→

While CR and DR pass through points that align with C or D, QR is the line drawn at an angle through E, which serves as the bisector.

So the correct answer is: QR←→