# Bookwork 1.5 Solutions 1.6 Power Point Guide Polygon (Poly means many) Soa polygon is a many sided closed figure. Examples: 1.6 Power Point Guide Lets categorize.. (dents/no dents)

A type of polygon with no dents A closed figure that is many sided 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 a. Some segments intersect more than two segments, so it is not a polygon.

b. The figure is a convex polygon. c. Part of the figure is not a segment, so it is not a polygon. d. The figure is a concave polygon. # of sides

3 4 5 6 7 8 9 10 12 n Type of Polygon

triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon dodecagon n-gon What is a polygon with 199 sides called? 199-gon

All sides are equal. Think lateral like a lateral pass in football All the sides are equal and all the interior angles are equal. All the interior angles

are equal. 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 a. The polygon has 6 sides. It is equilateral and equiangular, so it is a regular hexagon. b. The polygon has 4 sides, so it is a quadrilateral. It is not equilateral or equiangular, so it is not regular. 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 ALGEBRA A table is shaped like a regular hexagon.The expressions shown represent side lengths of the hexagonal table. Find the length of a side.