Question

Question: Liam is planning to construct a line segment bisector of
AB
on paper. 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?

Multiple Choice Options (Responses)
Option 1: 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”.

Option 2: 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
”.

Option 3: 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
”.

Option 4: Step #2 has a mistake. It should say: “Fold the paper along line segment
AB
”.

Answer 1

Correct choice: Option 3.

Reason: Folding A onto B produces a crease that meets AB at its midpoint C and is perpendicular to AB. Drawing the line through A, C, and B just reproduces AB, not the bisector. The correct step is to draw the line through C (the crease), not through A and B — that line is the perpendicular bisector of AB.