Question

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?

A. 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¯¯¯¯¯¯¯¯ .”
B. Step #2 has a mistake. It should say: “Fold the paper along line segment AB¯¯¯¯¯¯¯¯ .”
C. 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 .”
D. 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¯¯¯¯¯¯¯¯ .”

Answer 1

The mistake in Liam's steps is in **Step #4**.

A line segment bisector specifically needs to pass through the midpoint of the segment and be perpendicular to the segment itself. According to his folding method, point C is the midpoint of line segment AB, so the line should be drawn through C only.

Thus, the correct revision should be:

**A. 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¯¯¯¯¯¯¯¯.”**

This ensures that the line drawn is indeed the bisector, which divides the segment AB into two equal parts at point C.