Education Technology

Visiting the Rich History of Geometry using the TI-92

Published on 07/30/2005

Activity Overview

In this activity, students study various geometric theorems.

Before the Activity

  • Download TI Connect™ using the TI Connectivity Cable
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 3 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Understand the following geometric facts:

  • Given an orthocenter and three vertices of a triangle, any triangle formed by any three of these points will have the fourth point as its orthocenter

  • Euler Line:
  • In any triangle, the centroid, orthocenter, and the circumcenter are collinear, and the line is called the Euler line
  • The distance from the centroid to the orthocenter is twice the distance from the circumcenter to the centroid

  • Feuerbach Circle:
  • In any triangle, the midpoints of the sides, the feet of the altitudes, and the midpoints of the segments joining the vertices to the orthocenter all lie on a circle called the Nine Point circle or the Feuerbach Circle

  • Simpson Line:
  • Feet of the perpendiculars from any point on the circumcircle of a triangle to the sides of the triangle are collinear, and this line is called the Simpson Line

  • Midsegment's Theorem:
  • Segment joining the midpoints of any two sides of a triangle is parallel to and one-half the length of the third side

  • Varignon's Theorem:
  • Quadrilateral formed by joining the midpoints of the consecutive sides of any quadrilateral is a parallelogram

  • Golden Ratio:
  • A Golden Rectangle is one which can be dissected into a square and a rectangle similar to the original figure
  • After the Activity

    Students answer the questions on the activity sheet.

    Review student results:

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