__The
Final Project__

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### 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.

### 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 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.

### 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.

__Extensions__

### 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**

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