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