The Final Project


The purpose of this project is to provide interactive lessons and problem solving activities that can be used with the high school geometry student. These lessons and activities can be used with individual students on a personal computer or projected on a screen with an entire class during a lesson.

Rational of Project (a work in progress)

In the Intructional Unit, there are lessons that review area and perimeter of geometric figures and volume of solids. Probability of independent and dependent events are reviewed as well as the concept of a fair game. Finally, a lesson on geometric probability that ties the two topics together. Throughout each lesson are Geometer Sketchpad demonstrations to help the students visualize the problem. There are problem sets throughout the lesson which allows the students an opportunity to practice the problems.

The Instructional Unit

The problem solving activities address numerous ideas covered in the high school geometry class. Some problems require the use of concepts from algebra and trigonometry.

These problems are intended to be free-response questions that students should answer with justification.

Problem Solving


Extension problems are designed to enrich the traditional geometry course. This is especially useful when teaching gifted students. The topic are essays that instruct and illustrate various problems from geometry.


Napolean's Triangle

Pappas Area

Gergonne Point

Now that you have examined the above extensions see if you can discover Varignon's Theorem and write a GSP explanation.

1) Construct a trapezoid ABCD.

2) Find and label the midpoints of each side in order AB, BC, CD, and DA.

3) Define EFGH as a shape. (If any, what kind of quadrilateral does EFGH appear to be? It may require some measurements).

4) Using GSP to justify your conjecture. Explain in writing what you did to justify the conjecture.

5) Make a new sketch and construct your own quadrilateral. Again, find the midpoints of each side of your new quadrilateral and define this figure. Investigate this quadrilateral as you did above.

6) Have you discovered Varignon's Theorem?


If not, checkout the following website: The Theorem.


Other topics of interest to geometrical studies that may be used in the classroom.

Points of Concurrency related to Triangles

Side Side Angle Congruence (GSP4.0)

Medial Triangles

Tangent Circles and Loci

Constructing a Nine Point Circle

Pedal Triangle

Common Scripts for Geometry


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