Activity Overview
This activity illustrates the multiple representations of the attributes of triangles with their vertices on an equilateral hyperbola analytical, graphical and dynamic; addressing various conceptual levels of the students using CAS.
Before the Activity
Install the Cabri Geometry™ software on the computer
See the attached PDF file for detailed instructions for this activity
Print pages 1 - 4 from the attached PDF file for the class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Take any three points A, B, C on an equilateral hyperbola and find the orthocenter O of the triangle ABC
Note that the orthocenter is always a point on the hyperbola
Take any randomly chosen point on a random equilateral hyperbola and test this feature once more
Find a formula for the coordinates of the orthocenter of a triangle
Recognize a pattern in the results
Give a graphic representation of the triangle, the hyperbola, and the orthocenter
Find the circumcircle of the given triangle
Add the graph of this circle and point O which lies symmetric to orthocenter O with respect to the origin
Describe your results
Prove your conjecture
After the Activity
Review student results.
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary