6 1 Properties of Polygons Objectives Classify polygons

6. 1: Properties of Polygons Objectives Classify polygons based on their sides and angles.

Vocabulary Sketch Things to Remember Polygon A closed figure formed by 3 or more segments that intersect only at their endpoints. Diagonal A segment that connects non-consecutive vertices. Quadrilateral 4 A four-sided polygon. Pentagon 5 A five-sided polygon. Hexagon 6 A six-sided polygon.

Vocabulary Sketch Things to Remember Heptagon 7 A seven-sided polygon. Octagon 8 An eight-sided polygon. Nonagon 9 A nine-sided polygon. Decagon 10 A ten-sided polygon. Dodecagon 12 A twelve-sided polygon.

Vocabulary Sketch Things to Remember n-gon A polygon with n number of sides. Regular Polygon An equilateral AND equiangular polygon. Irregular Polygon Any polygon that is NOT regular. Concave Polygon Any part of the diagonal lies in the exterior of the polygon. Convex Polygon All diagonals lie in the interior of the polygon.

6. 1: Properties of Polygons Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.

Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. 1. polygon, hexagon

Example 1 B: Identifying Polygons Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. 2. polygon, heptagon

Example 1 C: Identifying Polygons Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides. 3. not a polygon

Check It Out! Example 1 a Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides. 4. not a polygon

Check It Out! Example 1 b Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides. 5. polygon, nonagon

Check It Out! Example 1 c Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides. 6. not a polygon

All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular. A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex.

7. Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, convex

8. Tell whether the polygon is regular or irregular Tell whether it is concave or convex. irregular, concave

9. Tell whether the polygon is regular or irregular Tell whether it is concave or convex. regular, convex

10. Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. regular, convex

11. Tell whether the polygon is regular or irregular. Tell whether it is concave or convex. irregular, concave