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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)
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