IM Geo.1.3 Lesson: Construction Techniques 1: Perpendicular Bisectors

Here are 2 points labeled A and B, and a line segment CD:

[size=150]Mark 5 points that are a distance [math]CD[/math] away from point [math]A[/math]. [br][/size][br]How could you describe all points that are a distance [math]CD[/math] away from point [math]A[/math]?

[size=150]Mark 5 points that are a distance [math]CD[/math] away from point [math]B[/math].[/size][br][br]How could you describe all points that are a distance [math]CD[/math] away from point [math]B[/math]?[br]

In a different color, mark all the points that are a distance [math]CD[/math] away from both [math]A[/math] and [math]B[/math] at the same time.

Your teacher will mark points A and B on the floor.

[br]Decide where to stand so you are the same distance from point [math]A[/math] as you are from point [math]B[/math]. Think of another place you could stand in case someone has already taken that spot.

After everyone sits down, draw a diagram of what happened.

In this activity, we thought about the set of points on the floor—a two-dimensional plane—that were equidistant from two given points A and B.

What would happen if we didn’t confine ourselves to the floor?

Start with two points [math]A[/math] and [math]B[/math] in three-dimensional space. What would the set of points equidistant from [math]A[/math] and [math]B[/math] look like?

Use the tools available to find the perpendicular bisector of segment PQ.

After coming up with a method, look for another method to find its perpendicular bisector.

Information: IM Geo.1.3 Lesson: Construction Techniques 1: Perpendicular Bisectors