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IGD Simson Line - Orthocenter

  • IGD: Simson Line - Orthocenter

    Grade: High School

    How is the Simson line of a triangle related to the orthocenter?

    Activity

    Instructions

    Point P is an arbitrary point on the circumcircle of the triangle. You can drag P to any location on the circumcircle, and you can move the vertices of the triangle.

    Exploration

    The thick orange line is the Simson line associated with P. Point H is the orthocenter of the triangle, and point S is the intersection of the Simson line and PH.
    • What is the relationship between HS and PS?
     

    Objectives and Standards

    NCTM Standards and Expectations
    • Geometry / Measurement
    • Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
    • High School (9-12)
    • Geometry