Question
Liam is planning to construct a line segment bisector of overline AB. . He plans to use the following steps: Step #1: Create line segment overline 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 overline AB. Which step has a mistake and how should the mistake be corrected?
Answers
GPT-4o mini
The mistake in Liam's steps lies in Step #4. The line he draws through points A, C, and B will not be a bisector of line segment overline AB. Instead, point C, as defined, is the midpoint of overline AB, and the correct bisector would be the perpendicular bisector, which also requires a different approach.
To correct the steps:
1. Step #1 remains the same: Create line segment overline AB on the paper.
2. Step #2 remains the same: Fold the paper so that point A is on top of point B.
3. Step #3 remains the same: Unfold the paper and label the intersection of the fold and the line segment with point C. Point C is indeed the midpoint of overline AB.
4. **Correction for Step #4:** Instead of drawing a line through points A, C, and B, Liam should draw a perpendicular line through point C. To do this correctly, he can use a compass to draw arcs above and below point C, ensuring they intersect at two points equidistant from C; then, connect those intersection points. This line will be the perpendicular bisector of overline AB.
This correction ensures that Liam accurately creates the bisector that is perpendicular to overline AB at its midpoint.
To correct the steps:
1. Step #1 remains the same: Create line segment overline AB on the paper.
2. Step #2 remains the same: Fold the paper so that point A is on top of point B.
3. Step #3 remains the same: Unfold the paper and label the intersection of the fold and the line segment with point C. Point C is indeed the midpoint of overline AB.
4. **Correction for Step #4:** Instead of drawing a line through points A, C, and B, Liam should draw a perpendicular line through point C. To do this correctly, he can use a compass to draw arcs above and below point C, ensuring they intersect at two points equidistant from C; then, connect those intersection points. This line will be the perpendicular bisector of overline AB.
This correction ensures that Liam accurately creates the bisector that is perpendicular to overline AB at its midpoint.