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Liam is planning to construct a line segment bisector of AB¯¯¯¯¯¯¯¯

. He plans to use the following steps:

Step #1: Create line segment AB¯¯¯¯¯¯¯¯
on my paper.

Step #2: Fold the paper so that point A
is on top of point B
.

Step #3: Unfold the paper and label the intersection of the fold and the line segment with point C
.

Step #4: Use a straight edge to draw a line that passes through points A
, C
, and B
. This line is a bisector of AB¯¯¯¯¯¯¯¯
.

Which step has a mistake and how should the mistake be corrected?

(1 point)
Responses

Step #2 has a mistake. It should say: “Fold the paper along line segment AB¯¯¯¯¯¯¯¯
.”
Step #2 has a mistake. It should say: “Fold the paper along line segment Modifying above upper A upper B with bar .”

Step #2 has a mistake. It should say: “Fold the paper so that point A
is on top of point B
. Then, fold the paper again so that the midpoint of AB¯¯¯¯¯¯¯¯
is on top of points A
and B
.”
Step #2 has a mistake. It should say: “Fold the paper so that point upper A is on top of point upper B . Then, fold the paper again so that the midpoint of Modifying above upper A upper B with bar is on top of points upper A and upper B .”

Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point A
and another line that passes through point B
. These lines are bisectors of AB¯¯¯¯¯¯¯¯
.”
Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point upper A and another line that passes through point upper B . These lines are bisectors of Modifying above upper A upper B with bar .”

Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point C
(but not points A
and B
). This line is a bisector of AB¯¯¯¯¯¯¯¯
.”

1 answer

The mistake is in Step #4. The step incorrectly states that a line drawn through points A, C, and B is a bisector of segment AB. However, a line bisector of a segment should only go through the midpoint of that segment.

The correct response should indicate that:

Step #4 has a mistake. It should say: “Use a straight edge to draw a line that passes through point C (the midpoint) and is perpendicular to the line segment AB. This line is the bisector of AB.”

So, while there are variations in the responses about drawing through A and B, it’s essential to clarify that the bisector should be related to the midpoint (C), which is derived from the proper folding.