In an earlier unit, students conjectured that they could construct a perpendicular bisector by finding points that were an equal distance from the two endpoints of the segment being bisected. In this lesson, they prove the Perpendicular Bisector Theorem, confirming their conjecture about equidistant points and perpendicular bisectors. The purpose of completing this proof now is to prepare to use the Perpendicular Bisector Theorem in the proof of the SideSideSide Triangle Congruence Theorem.
In this lesson, students write proofs of both directions of the Perpendicular Bisector Theorem. They look at sample student work, critique it, write their own proofs, and finally critique their partner’s proof (MP3). Syntheses focus on applying the Perpendicular Bisector Theorem and on what it means for two logical statements to be converses of one another. Two statements are converses if the “if” part and the “then” part are swapped.
Technology isn‘t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Lesson overview
 8.1 Warmup: Which One Doesn’t Belong: Intersecting Lines (5 minutes)

8.2 Activity: Lots of Lines (15 minutes)
 Includes "Are you Ready for More?" extension problem
 8.3 Activity: Not Too Close, Not Too Far (15 minutes)
 Lesson Synthesis
 8.4 Cooldown: Reflect and Revise (5 minutes)
Learning goals:
 Critique others' reasoning (in written language) about the Perpendicular Bisector Theorem.
 Prove (orally and in writing) the Perpendicular Bisector Theorem.
Learning goals (student facing):
 Let’s convince ourselves that what we’ve conjectured about perpendicular bisectors must be true.
Learning targets (student facing):
 I can critique an explanation of the Perpendicular Bisector Theorem.
 I can explain why the Perpendicular Bisector Theorem is true.
Required materials:
 Geometry toolkits
Required preparation:
 The student diagrams from a previous lesson‘s cooldown, Revisiting Perpendicular Bisectors, will be used in the Not Too Close, Not Too Far activity.
 Prepare additional copies of the Blank Reference Chart blackline master (double sided, 1 per student).
 Students can staple the new chart to their full ones, as they will need to continue to refer to the whole packet.
Glossary:
 converse  The converse of an ifthen statement is the statement that interchanges the hypothesis and the conclusion. For example, the converse of "if it's Tuesday, then this must be Belgium" is "if this is Belgium, then it must be Tuesday."
 Access the complete Geometry Course glossary.
Standards:
 This lesson builds on the standards: CCSS.7.G.B.5MS.7.G.5CCSS.HSGCO.A.4MS.GCO.4CCSS.HSGCO.B.6MS.GCO.6CCSS.HSGCO.D.12MS.GCO.12MO.7.GM.B.5MO.G.CO.A.4MO.G.CO.A.5MO.G.CO.B.6MO.G.CO.D.11
 This lesson builds towards the standards: CCSS.HSGCO.A.3MS.GCO.3CCSS.HSGCO.B.8MS.GCO.8CCSS.HSGCO.C.9MS.GCO.9MO.G.CO.A.3MO.G.CO.B.7MO.G.CO.C.8
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