Geometry Basics Unit Test

Question

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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

In this scenario, Lexi folded her paper so that point C was on top of point D, creating a line segment CD that was folded in half. The intersection of the fold with the segment indicates the midpoint of CD. Since the fold creates two equal segments, the line or segment that bisects CD would be the line QR through point E. However, since QR was drawn at an arbitrary angle and does not necessarily bisect CD directly, the correct bisector here is the line segment that passes through the midpoint created by the fold.

Therefore, the correct answer for the segment bisector in this scenario is:

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

This is because CD is the line segment that Lexi folded and the midpoint of CD represents the bisector of CD.