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?
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?
Answers
GPT-4o mini
The mistake is in Step #4. The line drawn through points A, C, and B will not necessarily be a bisector of line segment AB.
To correct this mistake, Step #4 should be modified as follows:
**Corrected Step #4:** Use a straight edge to draw a line through point C that is perpendicular to line segment AB. This line will bisect segment AB at point C.
The intersection point C, found from the fold, actually represents the midpoint of segment AB, and drawing a perpendicular line through C ensures that it is the bisector of AB.
To correct this mistake, Step #4 should be modified as follows:
**Corrected Step #4:** Use a straight edge to draw a line through point C that is perpendicular to line segment AB. This line will bisect segment AB at point C.
The intersection point C, found from the fold, actually represents the midpoint of segment AB, and drawing a perpendicular line through C ensures that it is the bisector of AB.