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

CD¯¯¯¯¯¯¯¯
line segment cap c cap d

DR←→
over left right arrow cap d cap r

CR←→
over left right arrow cap c cap r

QR←→
over left right arrow cap q cap r
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1 answer

In this scenario, Lexi folded the paper to bring point C to point D, creating a line of symmetry. The intersection point of the fold with the line segment is labeled point E, which becomes a significant reference point.

When she drew the line QR through point E, it creates a new line at an angle. However, the crucial aspect here revolves around the lines CR and DR that are drawn through points C and R, and points D and R respectively.

Since DR and CR are segments drawn from the endpoints of the base of the triangle (CD) to a point R and originate from the respective points C and D, the line segment that serves as the perpendicular bisector of CD (the base of the triangle) is indeed the line that corresponds to segments being equal distance from points C and D.

Given the context, the segment that serves as the bisector in this scenario is QR because it's drawn through point E (the intersection of the fold with CD), which acts as the bisector since it represents the line of symmetry for the folded triangle CD with R as the apex or an intersection point. Therefore, your answer would be:

  • QR←→ (line QR) is the bisector in this scenario.