Polygon 1.6 Power Point Guide (Poly – means “many”) Examples: So…a polygon is a many sided closed figure.

1.6 Power Point Guide

Let’s categorize….. (dents/no dents)

A closed figure that is “many” sided A type of polygon with no dents A type of polygon with dents (“think cave”)

EXAMPLE 1 Identify polygons Tell whether the figure is a polygon and whether it is convex or concave. a. b. c. d. SOLUTION Some segments intersect more than two segments, so it is not a polygon. a. b. The figure is a convex polygon. Part of the figure is not a segment, so it is not a polygon. c. d. The figure is a concave polygon.

# of sides Type of Polygon triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon dodecagon n-gon 3 4 5 6 7 8 9 10 12 n What is a polygon with 199 sides called? 199-gon

All the sides are equal and all the interior angles are equal. All sides are equal. All the interior angles are equal. Think “lateral” – like a lateral pass in football Here are some examples:

EXAMPLE 2 Classify polygons Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning. a. b. SOLUTION The polygon has 6 sides. It is equilateral and equiangular, so it is a regular hexagon. a. The polygon has 4 sides, so it is a quadrilateral. It is not equilateral or equiangular, so it is not regular. b.

EXAMPLE 2 Classify polygons Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning. c. c. The polygon has 12 sides, so it is a dodecagon. The sides are congruent, so it is equilateral. The polygon is not convex, so it is not regular.

EXAMPLE 3 Find side lengths A table is shaped like a regular hexagon.The expressions shown represent side lengths of the hexagonal table. Find the length of a side. ALGEBRA