Education Technology

Bring Geometry To Life

Published on 07/30/2005

Activity Overview

In this activity, students use the Geometer's Sketchpad application to construct Euler's Line, Pythagorean Proof, and Fermat's point. They also investigate the concept of perimeter.

Before the Activity

  • Install the The Geometer's Sketchpad application on the calculator using the TI Connect™ and the TI Connectivity Cable
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 8 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:
    Euler's Line:

  • Construct a triangle using The Geometer's Sketchpad
  • Draw the medians of the triangle and find their intersection point (the Centroid)
  • Draw the perpendicular bisectors of the triangle and find their intersection point (the Circumcenter)
  • Determine the intersection of altitudes (the Orthocenter)
  • Join these three points to create the Euler's line
  • Drag the vertices of the triangle to investigate the placement of the Euler's Line

  • Pythagorean Theorem:
  • Construct a right triangle using the Geometer's Sketchpad
  • Construct three squares formed by the sides of this triangle
  • Translate the small and medium squares into the large square
  • Note that the sum of the areas of the two smaller squares equals the area of the large square

  • Fermat's Point:
  • Create a triangle ABC and plot a point P inside it
  • Join the point to the vertices of the triangle
  • Mark vertex C as the center of rotation and rotate CP and PA 60° about C
  • Construct segment PP' and realize that CPP' is an equilateral triangle

  • Perimeter:
  • Construct a rectangle and a circle
  • Transfer the sum of the lengths of two of the rectangle's sides as the chord of the circle and plot a point on the chord
  • Create another chord passing through this point
  • Find a rectangle with fixed area but different perimeters
  • Understand that the rectangle will have maximum perimeter when the constructed chord is the diameter of the circle
  • 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