In this lesson, students prove the Perpendicular Bisector Theorem, confirming their conjecture about equidistant points and perpendicular bisectors. Students previously 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. This proof confirms that conjecture. 

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” parts and the “then” parts 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.

Math Community

The goal of today’s exercise is to use the suggestions from the previous exercise to revise the “Norms” sections of the Math Community Chart and to invite students to reflect on one norm that will be a strength for them. Both activities begin to build shared accountability for and investment in the classroom norms.