**Objectives:** Students
will explore the properties of polygons and develop their own
definitions for types of polygons. Students will also explore
and develop the idea of what it means to be a regular polygon.

**Materials:** GSP
file "Polygons" and "Regularpolys" and student
worksheet

NAME:___________________________

**Instructions:**
Open the GSP file "Polygons"
and use this file for problems 1 - 6.

**Polygons** are
closed figures made up of lines segments. There are several types
of polygons. This exploration will require that you use examples
of the types of polygons to develop definitions for the types
of polygons.

1. TRIANGLES

The GSP file shows three examples of triangles. What does it mean to be a triangle? What does the prefix "tri" mean? Write your own definition for the word "triangle."

2. QUADRILATERALS

The GSP file also has three examples of quadrilaterals shown. What do you notice about all of the quadrilaterals? What does it mean to be a quadrilateral? Write your own definition for "quadrilateral." What does the prefix "quad" mean?

3. PENTAGONS

Look at the examples of pentagons. What do all of the examples have in common? Write a definition of "pentagon."

4. HEXAGONS

Find the examples of hexagons. What do you notice about all of the hexagons. Write a definition for "hexagon."

5. SEPTAGONS

Look at the examples of the septagons and write your own definition for "septagon."

6. OCTAGONS

Do the same thing for the octagons as you have for all of the above; be sure to write a definition of the word "octagon."

Now open the GSP file "Regularpolys". Use this sketch to answer the following questions.

7. Look at the Regular Triangle. Measure its sides and angles. What do you notice about the properties of this triangle?

8. Measure the sides and angles of the Regular Quadrilateral. What do you notice?

9. Do the same for the Regular Pentagon. What do you see?

10. Explore the side lengths and angle measures for the Regular Hexagon. What do you find?

11. Write down what you think about the side lengths of the Regular Septagon and Regular Octagon. Use the Measure feature of GSP to check your conjecture about the side lengths of these two regular polygons.

12. Write down what you suspect about the angle measures of the Regular Septagon and Regular Octagon. Use GSP's measure feature to check your conjecture.

13. Write a sentence to describe what it means to be a regular polygon.