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… Quadrilateral

5 Sides… Pentagon

6 Sides… Hexagon

7 Sides… Heptagon

8 Sides… Octagon

9 Sides… 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.

The quadrilateral family tree:

1.

2.3. 4.

5.

6.

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

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

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

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

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

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

1 2

3 4

• 1 + 2 + 3 + 4 = 360°

Find the missing angles.

45° 55°

100° x°

118° 50°

80°y°

»This formula can be used to find the angle sum of any polygon:A = 180(n − 2)

AngleSum

Numberof Sides

A = 180(n − 2)A = 180(4 − 2)

A = 180(2)A = 360°

Divide byn to find

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

»A repetitive pattern of polygons that fit together with no overlaps or holes is called a tessellation.

5 × 2.4 = 12 m

»Find the measure of each interior angle, round to the nearest tenth if necessary.

BW: [10-6] Review

Regular dodecagon(12 sides)

Regular undecagon(11 sides)

34