Polygons

Polygons

»A polygon is a simple, closed figure formed by three or more straight lines.

»Examples: »Non-Examples:

»Polygons are named by the number of sides they have.

3 Sides… Triangle 4 Sides… 5 Sides… Quadrilateral Pentagon

6 Sides… 7 Sides… 8 Sides… 9 Sides… Hexagon Heptagon Octagon Nonagon

10 Sides… Decagon n Sides… n-gon Ex: 21-gon »A polygon that has all sides and angles congruent is called a regular polygon.

»Classify each polygon and state whether it is regular. If it is not a polygon, explain why.

1. A quadrilateral is a closed figure with four sides and four angles. 1.

The quadrilateral 6.

family tree: 2.

2. A parallelogram is a quadrilateral with two pair of parallel sides.

3. A rectangle is a quadrilateral with four right angles.

4. A rhombus is a quadrilateral with 4 congruent sides.

5. A square is a quadrilateral with 4 right angles and 4 congruent sides.

6. A trapezoid is a quadrilateral with 1 pair of parallel sides.

1 2 3 4

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The sum of the angles in any quadrilateral is always 360 °.

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1 + 2 + 3 + 4 = 360 °

Find the missing angles.

45 ° 55 ° 100 ° x ° 118 ° 80 ° y ° 50 °

»This formula can be used to find the angle sum of any polygon:

A = 180( n − 2) Angle Number Sum of Sides A = 180(n − 2) A = 180(4 − 2) Divide by n to find A = 180(2) A = 360 °

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each angle.

4 = 90 °

»Find the measure of each interior angle in a regular octagon.

»Perimeter is the distance around any polygon.

»What is the perimeter of this regular pentagon?

2.4 m 5 × 2.4 = 12 m »A repetitive pattern of polygons that fit together with no overlaps or holes is called a tessellation.

BW: [10-6] Review »Find the measure of each interior angle, round to the nearest tenth if necessary.

Regular Regular dodecagon (12 sides) undecagon (11 sides) 34