Aim: What are the formulas concerning the interior angles ...



Kathleen A. Farrell CSC 704

Professor Susan Imberman Spring 2010

Aim: What are the formulas concerning the interior angles of a polygon?

Objectives: Students will be able to…

1. Define equilateral polygon, equiangular polygon and regular polygon

2. Name polygons which have 4, 5, 6, 7, 8, 9, 10 sides

3. State formulas for:

• Sum of the measures of the interior angles of a polygon

• One interior angle of a regular n-gon

4. Apply the formulas in numerical and algebraic problems

Motivation:

1. If the sides of a polygon are congruent, are the angles also? Explain.

2. If the angles of a polygon are congruent, are the sides also? Explain

The above leads to 3 definitions:

1. An equilateral polygon is one with all of its sides congruent.

2. An equiangular polygon is one with all of its angles congruent.

3. If a polygon is both equilateral and equiangular then it is said to be a regular polygon.

Examples of 4 sided figures:

[pic]

Equilateral Equiangular Regular

What is the sum of the measures of the angles of a quadrilateral? (360°)

Demonstrate a quadrilateral can be divided into two disjoint (non-overlapping) triangles each with angle sum of 180°. Thus, we get a total of 360°

[pic]

Development:

Develop the following chart (using diagrams where needed) as shown in excel.

finalexcel.xls

Medial Summary: Use the power point below.

Summary.ppt

Applications:

1. Find the sum of the measures of the interior angles of a 52 sided polygon. (9000)

2. The sum of the measures of the interior angles of a polygon is 3600. Find the

number of sides in this polygon. (22)

3. If the measure of each interior angle of a regular polygon is 170, find the

number of sides. (26)

Final Summary:

1. Under what circumstances do we use the formula 180(n-2)? 180(n-2) ?

n

2. Why don’t we divide out the n’s in the second formula?

This lesson may be used in an eighth grade math class or in a 10th grade geometry class depending on the level of the students.

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