Lesson 3: Construction Techniques 1: Perpendicular Bisectors
About this lesson
The purpose of this lesson is to lay the foundation for understanding the perpendicular bisector of a segment as both a line perpendicular to a segment passing through its midpoint (by definition) and the set of points equidistant to the endpoints. The second fact will be proven in the next unit. The perpendicular bisector plays a key role in the definition of reflection later in this unit and in the proof of the SideSideSide triangle congruence theorem in the next unit.
This lesson continues the theme of asking how much can be learned without using numbers to measure distance as well as building on students’ understanding of angle and perpendicular from previous grades. Students look for and make use of structure when they think about where their classmates should stand during Human Perpendicular Bisector in order to be the same distance away from two given points (MP7). The more students that correctly place themselves, the more apparent the structure. Once students determine the structure, they record it as a conjecture. A conjecture is defined as a reasonable guess that students are trying to either prove or disprove.
If students have ready access to digital materials in class, they can choose to perform all construction activities with the GeoGebra Construction tool accessible in the Math Tools or available at https://www.geogebra.org/m/VQ57WNyR.
Lesson overview
 3.1 Warmup: Find All the Points! (5 minutes)

3.2 Activity: Human Perpendicular Bisector (15 minutes)
 Includes "Are you Ready for More?" extension problem
 3.3 Activity: How Well Can You Slice It? (15 minutes)
 Lesson Synthesis
 3.4 Cooldown: Walk the Line (5 minutes)
Learning goals:
 Comprehend that a perpendicular bisector is the set of points equidistant from two given points.
 Construct a perpendicular bisector.
Learning goals (student facing):
 Let’s explore equal distances.
Learning targets (student facing):
 I can construct a perpendicular bisector.
 I understand what is special about the set of points equidistant from two given points.
Required materials:
 Geometry toolkits
 Masking tape
 Measuring tapes
Required preparation:
 For Human Perpendicular Bisector, mark two points on the floor of the classroom two meters apart, using masking tape.
 Clear a large space around and between the two marked points.
Glossary:
 conjecture  A reasonable guess that you are trying to either prove or disprove.
 perpendicular bisector  The perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to it.
 Access the complete Geometry glossary.
Standards:
 This lesson builds towards the standards: CCSS.HSGCO.A.4MS.GCO.4CCSS.HSGCO.C.9MS.GCO.9CCSS.HSGCO.D.12MS.GCO.12MO.G.CO.A.4MO.G.CO.C.8MO.G.CO.D.11
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.