Stepping Stone 8: Construction Techniques 1: Perpendicular Bisectors
Learning Targets:
I can construct a perpendicular bisector.
I understand what is special about the set of points equidistant from two given points.
Vocabulary:
perpendicular bisector: The perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to it.
Standards Addressed:
G-CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G-CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Activity: Human Perpendicular Bisector
Your teacher will mark points A and B on the floor. Decide where to stand so you are the same distance from point A as you are from point B. 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.
Activity: How Well Can You Slice it?
The perpendicular bisector is a line through the midpoint of a segment that is perpendicular to that segment. Informally, bi means two and sect means cut, so a perpendicular bisector is literally a line perpendicular to a segment that cuts it into two congruent pieces.
Explain why each dashed line is not a perpendicular bisector of the segment it intersects.
What does this all mean?
This is a perpendicular bisector:
These are common ways to label this:
