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Section 7.4

Section 7.4 . Regular Polygons. 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?. Some more review.

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Section 7.4

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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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