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Understanding Regular Polygons: Formulas, Characteristics, and Examples

Explore the definition, formulas, and special names of regular polygons in this comprehensive review. Learn about interior and exterior angles, special characteristics, and how to calculate angles for different types of polygons.

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Understanding Regular Polygons: Formulas, Characteristics, and Examples

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  1. Section 7.4 Regular Polygons

  2. A little review • What is a polygon? • An enclosed figure that has at least three sides, all of which are segments • What is the formula for the number of diagonals of a polygon?

  3. Some more review • What is the formula for the sum of the interior angles of a polygon? • What do the exterior angles always add up to? • 360

  4. Special polygons • Some polygons have special characteristics • We have already discussed the special types of quadrilaterals • One quadrilateral in particular is especially interesting: • the square

  5. Regular polygons • What makes a polygon regular? • Let’s look at some examples to determine the answer. • A square is a regular polygon. • What do we know about squares?

  6. Another regular polygon • This is a regular hexagon. • What is special about this polygon? 120 120 120 120 120 120

  7. The definition • A regular polygon is a polygon that is both equilateral and equiangular. • In other words, all of the sides are congruent and all of the interior angles are congruent. • If only one of the conditions is met then it is not a regular polygon.

  8. Special names There are two regular polygons that have special names: • quadrilateral is a square • triangle is an equilateral triangle All other polygons are just called regular (i.e. regular hexagon)

  9. A formula for regular polygons • If we have a regular polygon we can find the measure of each exterior angle • where E is the measure of the angle and n is the number of sides • To find the interior angle you subtract the exterior angle from 180º.

  10. Examples • Find the exterior angle of a regular… • Decagon • Octagon • Dodecagon

  11. Examples • Find the interior angle of a regular… • Hexagon • Nonagon • Heptagon

  12. Examples • Find the number of sides a regular polygon has if each of its angles measures… • 60º • 150º • 168º

  13. Example • The sum of the measures of the angles of a regular polygon is 2340. Find the measure of each interior angle.

  14. Example • The ratio of a regular polygon’s interior angle to an exterior angle is 3:2. What is the name of this shape?

  15. ASN • A regular polygon is equiangular. • An equiangular polygon is regular. • The measure of the exterior angle of a regular polygon is less than the measure of the interior angle. • If the number of sides of a regular polygon is cut in half then the exterior angle measure remains the same.

  16. TF • The measure of the exterior angle of a regular polygon can never be the same as the measure of the interior angle. • As the number of sides of a regular polygon increases the measure of the exterior angle decreases. • A regular polygon can have an interior angle that measures less than 60º.

  17. Homework • p. 316-317 1-5, 10-12, 13 a-d

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