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The Simson Line

Activity Overview

Students study the Simson line and analyze the relationship it shares with its triangle.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print page 43 from the attached PDF file for your class

    • During the Activity

    Distribute the page to the class.

    Follow the Activity procedures:

  • Draw a triangle and construct its circumcircle
  • Place a point P anywhere on the circumcircle and hide the perpendicular bisectors
  • Extend the sides of the triangle
  • Draw perpendiculars from point P to the extended lines, and label the points of intersection
  • Observe that the 3 points are collinear, and understand that the line connecting these 3 points is called Simson Line or Wallace Line
  • Realize that if point P is on a vertex of the triangle, then two of the three points of intersection are located at the same vertex
  • Create a macro to explore which points on the circumcircle have a Simson line that passes through each of the sides of the triangle

    • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary

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